What Is Ohm’s Law? Explanation, Formula & Graph

In the vast and intricate world of electricity, Ohm’s Law stands as one of the most fundamental and crucial principles. Named after the German physicist Georg Simon Ohm, this law describes the relationship between three core quantities in an electrical circuit: Voltage, Current, and Resistance. For any student interested in physics concepts, whether you're tackling CBSE Class 10 or 12 Physics, preparing for JEE Mains and Advanced Physics, aspiring for NEET Physics, or getting ready for BITSAT Physics, a deep understanding of Ohm’s Law is indispensable.

This guide will take you through a detailed explanation of Ohm’s Law, its various formulae, and how to interpret its graph. We will delve into the individual components of Voltage (V), Current (I), and Resistance (R), providing analogies to make these abstract electrical concepts more concrete. Furthermore, we will explore the limitations of Ohm’s Law, its wide-ranging applications in real-world scenarios, and how it forms the bedrock for more advanced circuit analysis. For Indian students studying physics in USA, mastering Ohm's Law is not just about scoring well; it's about building foundational knowledge that will serve you throughout your academic and professional career in science and engineering.

Understanding Ohm’s Law is the gateway to comprehending how electrical energy flows and is utilized in everything from simple light bulbs to complex electronic devices. It’s the first step in truly grasping the dynamics of electrical circuits and preparing you for the challenges of JEE Physics and NEET Physics. Let's embark on this electrifying journey to demystify Ohm’s Law.

Before we dive into the Ohm's Law formula itself, it's essential to have a crystal-clear understanding of the three fundamental quantities it relates: Voltage, Current, and Resistance. These are the building blocks of any electrical circuit, and grasping their individual meanings is crucial for truly comprehending Ohm’s Law.

1. Voltage (V): The Driving Force

Voltage, often symbolized by 'V', is also known as potential difference or electromotive force (EMF) in some contexts. Imagine it as the "pressure" or "push" that forces electric charges (electrons) to move through a conductor. Without voltage, there would be no force to initiate or sustain the flow of current.

• Definition: Voltage is the work done per unit charge to move a charge from one point to another in an electric field. It represents the potential energy difference between two points.
• Unit: The standard unit for voltage is the Volt (V). One Volt is defined as one Joule of energy per Coulomb of charge ( 1V = 1 J/C ).
• Analogy (Water System): Think of a water pipe system. Voltage is analogous to the water pressure. The higher the pressure, the more force there is to push the water through the pipes. Similarly, a higher voltage provides a greater "push" for electrons.
• Importance for Exams: Understanding voltage is critical for CBSE Class 12 Physics, especially in chapters on electrostatics and current electricity. For JEE Physics and NEET Physics, questions often involve calculating potential differences across various components in complex circuits.

2. Current (I): The Flow of Charge

Current, symbolized by 'I' (from the French word "intensité"), is the actual flow of electric charge. In most conductors, this flow consists of electrons moving from a region of higher potential to a region of lower potential.

• Definition: Current is defined as the rate of flow of electric charge. Mathematically, it is I = Q/t , where Q is the charge and t is time.
• Unit: The standard unit for current is the Ampere (A). One Ampere is defined as one Coulomb of charge passing a point per second ( 1A = 1 C/s ).
• Analogy (Water System): In our water pipe analogy, current is like the volume of water flowing per unit time (e.g., liters per second). The more water flowing, the higher the current.
• Importance for Exams: Current calculations are central to almost all electrical circuit problems in CBSE, JEE, NEET, and BITSAT Physics. Concepts like current density and Kirchhoff's Current Law build upon this fundamental understanding.

3. Resistance (R): The Opposition to Flow

Resistance, symbolized by 'R', is the opposition that a material offers to the flow of electric current. It's like friction in a mechanical system. Every material has some degree of resistance, though some are much better conductors than others.

• Definition: Resistance is the ratio of the voltage across a conductor to the current flowing through it.
• Unit: The standard unit for resistance is the Ohm ( \Omega ), named after Georg Simon Ohm himself. One Ohm is defined as one Volt per Ampere ( 1\Omega = 1 V/A ).
• Analogy (Water System): Resistance in the water analogy is akin to the narrowness or roughness of the pipe. A narrow, rough pipe offers more resistance to water flow, just as a material with high resistance impedes the flow of current.
• Factors Affecting Resistance: For CBSE Class 10 and 12 Physics, it's crucial to know the factors affecting resistance:
  • Length ( L ): Resistance is directly proportional to the length of the conductor ( R \propto L ). Longer wires have more resistance.
  • Area of Cross-section ( A ): Resistance is inversely proportional to the area of cross-section of the conductor ( R \propto 1/A ). Thicker wires have less resistance.
  • Material (Resistivity, \rho ): Resistance depends on the nature of the material, quantified by its resistivity ( \rho ). Conductors like copper have low resistivity, while insulators like rubber have very high resistivity. The formula for resistance based on these factors is: R = \rho L/A .
  • Temperature: For most metallic conductors, resistance increases with temperature.
• Importance for Exams: Resistance is a key concept for all competitive exams. Questions on series and parallel combinations of resistors, heating effects of current, and material properties (like resistivity) are common in JEE Physics, NEET Physics, and BITSAT Physics.

With these foundational physics concepts firmly in mind, we are now ready to fully appreciate the elegant relationship that Ohm’s Law defines between them. This is the cornerstone for understanding any electrical circuit.

At its core, Ohm’s Law states that the current flowing through a conductor between two points is directly proportional to the voltage across the two points, and inversely proportional to the resistance between them, provided the temperature and other physical conditions remain constant. This simple yet powerful statement can be expressed as a mathematical formula.

The Primary Ohm's Law Formula

The most common and fundamental Ohm’s Law formula is:

Where:

• V = Voltage (measured in Volts, V)
• I = Current (measured in Amperes, A)
• R = Resistance (measured in Ohms, \Omega )

This formula directly tells us that if you increase the voltage across a fixed resistance, the current flowing through it will increase proportionally. Similarly, if you increase the resistance for a given voltage, the current will decrease. This proportional relationship is a cornerstone of electrical circuits and is a frequently tested physics concept in CBSE, JEE, NEET, and BITSAT Physics exams.

Rearranging the Formula: Finding Any Variable

From the primary formula V = IR , we can easily derive the formulae to find Current or Resistance if the other two quantities are known. These derivations are straightforward algebraic manipulations, highlighting the versatility of Ohm’s Law in circuit analysis.

• To find Current ( I ): If you know the voltage ( V ) and resistance ( R ), you can calculate the current ( I ) using:

  I = V/R

  This means that for a constant voltage, as resistance increases, current decreases. This is a common scenario in everyday electronics where varying resistance (e.g., in a dimmer switch) changes the current and thus the brightness of a light.
• To find Resistance ( R ): If you know the voltage ( V ) and current ( I ), you can calculate the resistance ( R ) using:

  R = V/I

  This formula is particularly useful for determining the unknown resistance of a component when you can measure the voltage across it and the current flowing through it. It's often used in labs for Class 12 Physics CBSE experiments.

The Ohm's Law Triangle: A Handy Mnemonic

For many students, especially those in CBSE Class 10 and 12 Physics, the Ohm's Law Triangle (or Ohm's Law Pyramid) is a helpful mnemonic device to remember the three forms of the formula without having to rearrange them algebraically.

To use the triangle:

• Cover the variable you want to find.
• The remaining two variables in the triangle show you the formula.
  • Cover V: I \times R (meaning V = IR )
  • Cover I: V / R (meaning I = V/R )
  • Cover R: V / I (meaning R = V/I )

While simple, mastering these formulae and their applications is crucial for solving numerical problems in electrical circuits. This foundational knowledge is directly applied in JEE Mains Physics, where speed and accuracy in calculations are paramount, and in NEET Physics for direct formula-based questions. For BITSAT Physics, rapid recall and application of these formulae under timed conditions are key for effective time management strategies.

Beyond the mathematical formula, Ohm’s Law can also be beautifully represented visually through a V-I graph (Voltage vs. Current graph). This graphical explanation is particularly important for understanding the behavior of electrical circuits and differentiating between ohmic and non-ohmic conductors.

The Linear Relationship for Ohmic Conductors

For materials that obey Ohm’s Law (known as ohmic conductors), the voltage across the conductor is directly proportional to the current flowing through it, assuming constant physical conditions like temperature.

• If we plot Voltage (V) on the y-axis and Current (I) on the x-axis, the graph for an ohmic conductor will be a straight line passing through the origin.
• The slope of this V-I graph ( V/I ) directly represents the resistance (R) of the conductor. Since R = V/I , a steeper slope indicates higher resistance, and a gentler slope indicates lower resistance.

This linear graph is a strong indicator of Ohm’s Law being followed. Examples of ohmic conductors typically include metallic wires at constant temperature. This graphical representation is a standard topic in CBSE Class 12 Physics and is often tested in JEE Mains Physics and NEET Physics for identifying resistor properties.

Non-Ohmic Conductors: Deviations from Linearity

Not all materials obey Ohm’s Law perfectly. These are called non-ohmic conductors. For these materials, the V-I graph is not a straight line, meaning the resistance is not constant but changes with voltage or current.

• Semiconductors (e.g., Diodes, Transistors): These are classic examples of non-ohmic conductors. Their V-I graph is typically non-linear and asymmetrical, demonstrating different resistance characteristics depending on the direction and magnitude of the applied voltage. Their resistance often decreases as voltage increases beyond a certain point.
• Filament Lamps (Bulbs): As current increases through a filament lamp, its temperature rises significantly. Since the resistance of the metal filament increases with temperature, the V-I graph for a filament lamp will curve, showing an increasing slope (increasing resistance) as voltage and current increase.
• Electrolytes: Solutions that conduct electricity also exhibit non-ohmic behavior due to complex ionic movements.
• Gas Discharge Tubes: These devices also show non-linear V-I characteristics.

Understanding the V-I graph for both ohmic and non-ohmic conductors is a critical skill for CBSE Class 12 Physics students, and especially for those preparing for JEE Advanced Physics and NEET Physics, where distinguishing between these behaviors and analyzing their graphs is frequently tested. It showcases the limitations of Ohm’s Law and introduces the complexities of real-world electrical components.

For BITSAT Physics, conceptual questions involving interpreting these graphs and their implications for device behavior are common. This visual aspect of Ohm’s Law reinforces its practical significance in electrical circuits and electronics.

While Ohm’s Law is a cornerstone of electrical circuits and forms the basis of countless calculations, it's crucial for students to understand its limitations. Ohm’s Law is not a universal law for all materials and conditions. It specifically applies to ohmic conductors under constant physical conditions. For CBSE Class 12 Physics, JEE Physics, NEET Physics, and BITSAT Physics, knowing when and why Ohm’s Law deviates is as important as knowing when it applies.

The primary condition for Ohm’s Law to be valid is that the temperature and other physical conditions (like pressure, strain, light intensity for photosensitive materials) of the conductor remain constant. Any significant change in these conditions can lead to a deviation from the linear V-I graph expected from an ohmic conductor.

Key Scenarios Where Ohm's Law Fails:

• Temperature Dependence: For most metallic conductors, resistance increases with temperature. When a large current flows through a wire (like the filament in an incandescent bulb), the wire heats up. This increase in temperature causes its resistance to increase, meaning the ratio V/I is no longer constant. The V-I graph for such a device curves, as discussed in the previous section. This is a common example to illustrate the limitations of Ohm’s Law for CBSE Class 12 Physics.
• Semiconductor Devices: Devices made from semiconductors, such as diodes (e.g., p-n junction diode) and transistors, are inherently non-ohmic conductors.
  • Diodes: A diode's V-I characteristic is highly non-linear. In forward bias, it starts conducting significantly only after a certain threshold voltage (knee voltage) is reached, and then the current rises exponentially. In reverse bias, almost no current flows until breakdown voltage is reached. This behavior clearly violates the linear relationship of Ohm’s Law. Understanding these non-ohmic devices is crucial for JEE Advanced Physics and NEET Physics, as they are a significant part of modern electronics and solid-state physics curricula.
  • Thermistors: These are resistors whose resistance is highly dependent on temperature. They are used in temperature sensing and control.
• Unilateral Circuits: Circuits or devices that allow current to flow only in one direction, or offer different resistance for different directions of current. Diodes are prime examples of unilateral devices. Ohm’s Law applies to bilateral devices, where the magnitude of current is the same for the same voltage magnitude, regardless of polarity.
• Non-linear Elements: Elements where the relationship between V and I is not linear, or where voltage and current do not change proportionally. Examples include gas discharge tubes, vacuum tubes, and components operating under very high voltage or current conditions.
• Material Properties Changing with Voltage/Current: In some cases, the physical properties of the material itself can change under extreme voltage or current, altering its resistance.

For JEE Advanced Physics, understanding these limitations is key to analyzing more complex circuits that incorporate semiconductor devices. NEET Physics and BITSAT Physics might include conceptual questions about identifying ohmic vs. non-ohmic behavior based on V-I graphs.

In summary, while Ohm’s Law provides a simple and powerful model for many electrical circuits, it is an empirical law derived from observations, not a fundamental law of nature like the conservation of energy. Therefore, it has specific applicability conditions that must be considered.

Despite its limitations, the applications of Ohm’s Law are pervasive across almost every aspect of electrical engineering and basic electronics. It's an indispensable tool for designing, analyzing, and troubleshooting electrical circuits. For students of CBSE Physics, JEE Physics, NEET Physics, and BITSAT Physics, understanding these applications not only helps in solving physics numericals but also in appreciating the real-world relevance of this fundamental physics concept.

1. Simple Circuit Analysis

The most direct application is in analyzing simple circuits. Given any two of the three quantities (voltage, current, resistance), you can find the third.

• Calculating Current: If a 12V battery is connected across a 4\Omega resistor, the current is I = V/R = 12V / 4\Omega = 3A . This is a basic problem for CBSE Class 10 and 12 Physics.
• Calculating Resistance: If 0.5A of current flows through a bulb when 2.5V is applied across it, its resistance is R = V/I = 2.5V / 0.5A = 5\Omega .
• Calculating Voltage: If a 10\Omega resistor has 2A of current flowing through it, the voltage drop across it is V = IR = 2A \times 10\Omega = 20V .

These direct applications form the bedrock for more complex circuit analysis problems found in JEE Mains Physics and NEET Physics.

2. Designing Electrical Circuits

Engineers and hobbyists use Ohm’s Law extensively in designing electrical circuits.

• Choosing Resistors: To limit current to a specific level for sensitive components like LEDs, the appropriate resistance can be calculated using Ohm’s Law.
• Power Calculations: Ohm’s Law is combined with the formula for electrical power ( P = VI ) to determine the power dissipated by components. By substituting V or I from Ohm's Law, we get P = I^2R or P = V^2/R . This is crucial for JEE Physics and NEET Physics problems involving electrical energy and heating effects.

3. Safety Measures: Fuses and Circuit Breakers

Ohm’s Law is fundamental to understanding how safety devices like fuses and circuit breakers work. These devices are designed to protect electrical circuits from excessive current (overload) which can cause overheating and fire hazards.

• A fuse is a short piece of wire with a very low melting point. If the current ( I ) in the circuit exceeds a safe limit (due to low resistance, e.g., a short circuit), the heat generated ( I^2R ) melts the fuse, breaking the circuit and preventing damage to appliances or wiring. The rating of a fuse is determined by the maximum safe current it can carry based on Ohm's Law and power dissipation.

This practical application of Ohm’s Law is highly relevant for CBSE Class 10 and 12 Physics, often appearing in questions about household wiring and safety.

4. Voltage Dividers and Current Dividers

In more complex electrical circuits, Ohm’s Law is used in conjunction with Kirchhoff’s Laws to analyze voltage dividers and current dividers.

• Voltage Divider: Used to produce a fraction of the input voltage. The voltage across any resistor in a series circuit can be found using Ohm’s Law ( V_{resistor} = I_{total} \times R_{resistor} ). This is a key concept for JEE Advanced Physics.
• Current Divider: Used to split the total current among parallel branches. Ohm’s Law helps determine the current through each parallel branch given its resistance and the voltage across the parallel combination.

5. Sensor Applications

Many sensors operate on the principle of changing resistance in response to a physical quantity (e.g., temperature, light, pressure). By measuring the change in current or voltage across such a sensor (using Ohm’s Law), the physical quantity can be determined. Examples include:

• Thermistors: Resistance changes with temperature.
• LDRs (Light Dependent Resistors): Resistance changes with light intensity.

These introduce more complex applications relevant for JEE Advanced Physics and advanced topics in BITSAT Physics.

From the simplest flashlight to the most sophisticated computer chips, the principles of Ohm’s Law are at play. Mastering its formulae, understanding its graph, and recognizing its diverse applications provides students with a powerful toolkit for excelling in physics examinations and beyond. These concepts are fundamental to any practical electrical circuit endeavor.

For CBSE students in USA, Ohm’s Law is a foundational topic taught from an early stage, typically introduced in Class 10 Science (Physics) and then explored in much greater depth in CBSE Class 12 Physics. A solid understanding here is crucial not just for board exams but also as a stepping stone for competitive exams like JEE, NEET, and BITSAT.

Class 10 Physics (Brief Introduction)

• Basic definition of Ohm’s Law and the formula V=IR .
• Simple numerical problems involving direct application of the formula.
• Introduction to Voltage, Current, and Resistance and their units.
• Understanding V-I graphs for ohmic conductors (straight line).
• Factors affecting resistance (length, area, material, temperature).

Class 12 Physics (In-Depth Coverage)

In CBSE Class 12 Physics, Ohm’s Law is covered extensively in the unit on "Current Electricity." This is where students truly delve into the nuances and applications.

• Microscopic Form of Ohm's Law: Understanding the relationship between current density (j), conductivity ( \sigma ), and electric field (E): \vec{j} = \sigma \vec{E} . This shows how Ohm’s Law arises from the motion of electrons in a conductor.
• Drift Velocity: Linking current to the drift velocity of electrons.
• Temperature Dependence of Resistance: Detailed study of how resistance changes with temperature for metals, semiconductors, and alloys. This is crucial for understanding the limitations of Ohm’s Law.
• Series and Parallel Combinations of Resistors: Derivations of equivalent resistance for series and parallel circuits using Ohm’s Law as a fundamental tool.
  • Series: R_{eq} = R_1 + R_2 + ...
  • Parallel: 1/R_{eq} = 1/R_1 + 1/R_2 + ...
• Internal Resistance of a Cell: Applying Ohm’s Law to analyze circuits with real batteries, considering their internal resistance.
• Kirchhoff's Laws: While separate from Ohm’s Law, Kirchhoff's current and voltage laws are used extensively *with* Ohm’s Law to solve complex networks. For CBSE Class 12 Physics, students are expected to solve numericals using these combined principles.
• Power and Energy in Electrical Circuits: Using Ohm’s Law ( V=IR ) to derive power formulae ( P=VI=I^2R=V^2/R ) and calculate electrical energy consumption.
• Numerical Problems: A wide range of physics numericals, from direct applications to complex network analysis and problems involving combination of resistors, heating effects, and internal resistance.
• Experimental Verification: Understanding the experimental setup and procedure to verify Ohm’s Law in the lab.

For CBSE students in USA, our physics tuition USA provides comprehensive study materials and guidance specifically aligned with the CBSE syllabus. We ensure that every nuance of Ohm’s Law, from its theoretical explanation to its practical applications and limitations, is thoroughly understood, preparing students for both board exams and competitive entrance examinations. This solid grounding in electrical concepts is paramount.

For students in the USA aiming for premier engineering and medical institutions in India, a robust understanding of Ohm’s Law is not merely academic; it's a critical component of their strategic preparation for JEE Mains and Advanced Physics, NEET Physics, and BITSAT Physics. While the core physics concept remains the same, the complexity and types of questions differ significantly across these exams.

JEE Mains and Advanced Physics: Deep Dive into Circuit Analysis

In JEE Physics, Ohm’s Law is not just tested in isolation but is intricately woven into complex circuit analysis problems.

• Complex Network Analysis: Expect problems involving multiple resistors, batteries (with internal resistance), and sometimes capacitors and inductors (though for steady-state DC circuits, they act as open/short circuits respectively). Ohm’s Law is used in conjunction with Kirchhoff's laws (Junction Rule and Loop Rule) to find currents through branches or voltage drops across specific components.
• Symmetry and Equivalent Resistance: JEE Advanced Physics often features problems where the direct application of series/parallel formulae is insufficient. Students need to apply concepts like Wheatstone bridge, symmetry, or star-delta transformations, all of which ultimately rely on Ohm’s Law for individual resistance calculations.
• Heating Effect of Current: Problems involving the heating effect of current ( H = I^2Rt ) and electrical power dissipation are common. These require precise calculations of current and resistance using Ohm’s Law.
• Potentiometer and Meter Bridge: These experimental setups are often featured in JEE Physics. While they involve null deflection methods, the underlying principles of potential difference and resistance per unit length are governed by Ohm’s Law.
• Graphical Analysis: Questions asking to interpret V-I graphs for different materials, including non-ohmic conductors like diodes and thermistors, are frequent. This tests a deeper understanding of Ohm’s Law’s limitations.

Success in JEE Physics requires not just knowing the formulae, but the ability to apply them strategically to solve complex physics numericals and conceptual challenges under time pressure.

NEET Physics: Accuracy and Conceptual Application

For NEET Physics, the focus on Ohm’s Law is more direct and application-oriented, often involving straightforward calculations and conceptual clarity.

• Direct Formula Application: Many questions will involve direct application of V=IR , I=V/R , or R=V/I . Speed and accuracy in these calculations are paramount due to the high volume of questions in a limited time.
• Series and Parallel Circuits: Problems on equivalent resistance for series and parallel combinations are very common. Students need to quickly identify the configuration and apply the correct formulae.
• Heating Effect and Power: Calculations of heat produced ( H = I^2Rt ) and power dissipated ( P=VI ) are frequently asked.
• Graphical Interpretation: Basic V-I graph interpretation, identifying ohmic vs. non-ohmic behavior, and calculating resistance from the slope.
• Factors Affecting Resistance: Questions based on the formula R = \rho L/A and how changes in physical dimensions or material affect resistance.

NEET Physics emphasizes strong foundational knowledge and efficient problem-solving. While the problems may not be as complex as JEE Advanced Physics, the need for rapid and accurate answers makes thorough practice essential.

BITSAT Physics: Speed and Conceptual Agility

BITSAT Physics tests a broad range of physics concepts with an emphasis on speed and conceptual agility. Ohm’s Law is frequently tested in this context.

• Quick Conceptual Checks: Many questions might be conceptual, requiring a clear understanding of the definition of Ohm’s Law, its limitations, and the basic properties of voltage, current, and resistance.
• Integrated Problems: Problems that combine Ohm’s Law with other topics like calorimetry (heating effect), basic kinematics (drift velocity), or optics (if components like LDRs are involved).
• Data Interpretation: Questions might present data tables of V vs. I and ask students to determine if a component is ohmic or calculate its resistance.
• Time Management: The sheer number of questions in BITSAT makes time management strategies crucial. Students must be able to recognize problem types and apply Ohm’s Law formulae quickly and accurately.

For all these competitive exams, access to specialized physics study material, consistent practice with past year papers, and targeted mock tests are invaluable. Our programs provide comprehensive resources and expert guidance to ensure CBSE students in USA are fully prepared to leverage their knowledge of Ohm’s Law to excel.

The best way to solidify your understanding of Ohm’s Law is through practice. Here are a few solved examples, ranging from basic CBSE Class 10/12 Physics level to more complex problems relevant for JEE and NEET Physics. These problems will help you apply the formula V=IR and its variations, alongside other core physics concepts.

Example 1: Basic Application (CBSE Level)

Problem: A simple electrical circuit consists of a 10\Omega resistor connected to a 20V battery. Calculate the current flowing through the resistor.

Solution:

• Given:
  • Voltage ( V ) = 20 V
  • Resistance ( R ) = 10\Omega
• Using Ohm’s Law formula I = V/R :

  I = 20V / 10\Omega = 2A

• Answer: The current flowing through the resistor is 2 Amperes.

Example 2: Series Circuit (CBSE / NEET Level)

Problem: Two resistors, R_1 = 5\Omega and R_2 = 15\Omega , are connected in series to a 60V power supply. Find the total current in the circuit and the voltage drop across each resistor.

Solution:

• First, find the equivalent resistance ( R_{eq} ) for series combination:

  R_{eq} = R_1 + R_2 = 5\Omega + 15\Omega = 20\Omega

• Next, calculate the total current ( I_{total} ) using Ohm’s Law:

  I_{total} = V_{total} / R_{eq} = 60V / 20\Omega = 3A

  In a series circuit, the current is the same through all components. So, I_1 = I_2 = 3A .
• Now, calculate the voltage drop across each resistor using Ohm’s Law ( V = IR ):
  • Voltage across R_1 : V_1 = I_1 \times R_1 = 3A \times 5\Omega = 15V
  • Voltage across R_2 : V_2 = I_2 \times R_2 = 3A \times 15\Omega = 45V
• Check: V_1 + V_2 = 15V + 45V = 60V , which matches the total supply voltage.

Example 3: Parallel Circuit (CBSE / JEE Mains Level)

Problem: Three resistors, R_1 = 6\Omega , R_2 = 3\Omega , and R_3 = 2\Omega , are connected in parallel to a 12V battery. Calculate the equivalent resistance, the total current, and the current through each resistor.

Solution:

• First, find the equivalent resistance ( R_{eq} ) for parallel combination:

  1/R_{eq} = 1/R_1 + 1/R_2 + 1/R_3 = 1/6 + 1/3 + 1/2 = (1 + 2 + 3)/6 = 6/6 = 1

  R_{eq} = 1\Omega

• Next, calculate the total current ( I_{total} ) using Ohm’s Law:

  I_{total} = V_{total} / R_{eq} = 12V / 1\Omega = 12A

• Now, calculate the current through each resistor. In a parallel circuit, the voltage across each branch is the same as the total supply voltage (12V):
  • Current through R_1 : I_1 = V_{total} / R_1 = 12V / 6\Omega = 2A
  • Current through R_2 : I_2 = V_{total} / R_2 = 12V / 3\Omega = 4A
  • Current through R_3 : I_3 = V_{total} / R_3 = 12V / 2\Omega = 6A
• Check: I_1 + I_2 + I_3 = 2A + 4A + 6A = 12A , which matches the total current (Kirchhoff's Current Law).

Example 4: Power Dissipation (JEE / NEET Level)

Problem: A 50\Omega heating element is connected to a 220V power supply. Calculate the power dissipated by the heating element and the electrical energy consumed in 30 minutes.

Solution:

• Given:
  • Resistance ( R ) = 50\Omega
  • Voltage ( V ) = 220 V
  • Time ( t ) = 30 minutes = 30 \times 60 = 1800 seconds
• Calculate Power ( P ) using Ohm’s Law variant P = V^2/R :

  P = (220V)^2 / 50\Omega = 48400 / 50 = 968W

• Calculate Electrical Energy consumed ( E ) using E = P \times t :

  E = 968W \times 1800s = 1742400 J

  E = 1.7424 \times 10^6 J (or 1.7424 MJ)

• Answer: The power dissipated is 968 Watts, and the electrical energy consumed in 30 minutes is 1.7424 \times 10^6 Joules.

These examples demonstrate how Ohm’s Law is applied in various contexts. Regular practice of such physics numericals is essential for students preparing for CBSE, JEE, NEET, and BITSAT Physics, reinforcing both conceptual clarity and problem-solving skills. Utilize our physics study material and past year papers for more practice.