How to Apply Ohm's Law: Formula, Units, and Example Problems
Ohm’s Law is a fundamental principle in the study of electricity. It describes the relationship between voltage, current, and resistance in an electrical circuit. Discovered by Georg Simon Ohm, this law forms the basis of understanding how electric circuits behave, making it essential for both students and anyone interested in electronics.
When a conductive path is created for electric charge to move, it establishes an electric circuit. The continuous movement of charge (current) through the circuit can be compared to the flow of water through a pipe. The driving force for this movement is called voltage, while the obstruction encountered by the current is known as resistance.
Understanding Voltage, Current, and Resistance
Voltage is a measure of the potential energy that motivates charge carriers to move between two points in a circuit. Current is the rate at which electric charge flows through a conductor, and resistance is the opposition that current faces as it moves through a material.
Each of these quantities is measured using standardized units. Voltage is measured in volts (V), current in amperes (A), and resistance in ohms (Ω). These units are named after pioneers in the field: Volta, Ampere, and Ohm. In equations, voltage may be represented as “V” or “E” (with E usually referring to electromotive force), current as “I,” and resistance as “R.”
The Ohm’s Law Equation and Triangle
Ohm’s Law states that for a given temperature, the current (I) through a conductor between two points is directly proportional to the voltage (V or E) across those points, and inversely proportional to the resistance (R) in the path. The core mathematical expression is
| Relationship | Equation | Variable Solved |
|---|---|---|
| Ohm’s Law | E = I × R | Voltage |
| Current formula | I = E / R | Current |
| Resistance formula | R = E / I | Resistance |
A convenient way to remember these relationships is the Ohm’s Law Triangle. Place the letters E, I, and R inside a triangle: cover the unknown variable, and the remaining two show the operation. For example, cover R to get R = E/I.
Units of Measurement in Electrical Circuits
| Quantity | Symbol | SI Unit |
|---|---|---|
| Voltage | V or E | Volt (V) |
| Current | I | Ampere (A) |
| Resistance | R | Ohm (Ω) |
Example Problems Using Ohm’s Law
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Example 1: If a lamp in a circuit has a resistance of 8 Ω and is connected across a 12 V battery, what is the current through the lamp?
Solution: Use I = E / R = 12 V / 8 Ω = 1.5 A
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Example 2: A circuit allows a current of 3 A when supplied with 9 V. What is the resistance?
Solution: Use R = E / I = 9 V / 3 A = 3 Ω
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Example 3: In a simple circuit, if the resistance is 5 Ω and current is 2 A, what is the voltage supplied?
Solution: Use E = I × R = 2 A × 5 Ω = 10 V
Stepwise Approach to Circuit Analysis
- Identify known values (voltage, current, resistance).
- Select the appropriate form of Ohm’s Law.
- Substitute the known values into the equation.
- Solve algebraically for the unknown variable.
- Check units carefully for consistency.
More on Electric Charge and Its Measurement
The fundamental unit of electric charge is the coulomb (C). A current of 1 ampere represents the flow of 1 coulomb of charge per second. Voltage is the potential energy per unit charge, with 1 volt defined as 1 joule per coulomb.
Practical Application and Concept Review
- Voltage, current, and resistance are interconnected: altering one affects the others in a circuit.
- Ohm’s Law is essential for predicting how circuits will respond to changes in voltage or resistance.
- Mastery of these concepts is crucial for designing, analyzing, and troubleshooting circuits.
| Summary Points |
|---|
| Voltage is measured in volts (E or V). |
| Current is measured in amperes (I). |
| Resistance is measured in ohms (R). |
| Core formula: E = I × R ; I = E / R ; R = E / I. |
To deepen your understanding, explore more about Ohm’s Law concepts and applications or see how resistors work at Vedantu Resistor page. For practice questions and interactive learning, visit Electric Circuits and Electric Current resources.
Mastering Ohm’s Law is a stepping stone towards understanding the broader domain of electricity and electronics.
FAQs on Understanding Ohm's Law and Resistance in Physics
1. What is Ohm’s Law in simple words?
Ohm’s Law states that the electric current (I) passing through a conductor is directly proportional to the potential difference (V) across its ends, provided temperature remains constant. The mathematical form is V = I × R, where R is resistance.
2. What is the formula for resistance using Ohm’s Law?
According to Ohm’s Law, resistance (R) can be calculated by dividing the voltage (V) by the current (I):
R = V / I
This formula helps find the resistance when voltage and current are known.
3. What is the SI unit of resistance?
The SI unit of resistance is the ohm (Ω).
One ohm is defined as the resistance when a current of one ampere flows under a potential difference of one volt.
4. How do you verify Ohm’s Law in a laboratory experiment?
Ohm’s Law can be verified by following these steps:
• Connect a circuit with a known resistor, ammeter, voltmeter, and variable voltage source.
• Vary the voltage and record the current readings.
• Plot voltage (V) on the x-axis and current (I) on the y-axis.
• If the graph is a straight line passing through the origin, Ohm’s Law is verified.
5. What are the factors affecting resistance of a conductor?
Resistance (R) of a conductor depends on:
• Length (R ∝ L): Longer conductors have higher resistance.
• Cross-sectional area (R ∝ 1/A): Thicker conductors have lower resistance.
• Nature of material: Different materials have different resistivities.
• Temperature: Resistance usually increases with temperature in metals.
6. What is the difference between resistance and resistivity?
Resistance (R) is the opposition to current flow in a specific object, measured in ohms (Ω).
Resistivity (ρ) is a property of the material itself, independent of length or area, measured in ohm-meter (Ω·m).
• Resistance depends on length, area, and material.
• Resistivity depends only on the material and temperature.
7. What happens to the current in a circuit if resistance is doubled but voltage remains the same?
If resistance is doubled and voltage remains constant, the current becomes half.
This is because I = V / R; increasing R decreases I proportionally.
8. How are resistors connected in series and parallel? What are the formulas?
Series:
Rtotal = R1 + R2 + ...
Parallel:
1/Rtotal = 1/R1 + 1/R2 + ...
Series increases total resistance; parallel decreases it.
9. Can all materials obey Ohm’s Law? What are ohmic and non-ohmic conductors?
Not all materials obey Ohm’s Law. Materials that show a linear V-I relationship (constant resistance) are called ohmic conductors (like metals). Others, which do not have constant resistance (e.g., diodes, filament bulbs), are non-ohmic conductors.
10. Why do we use the Ohm's Law triangle?
The Ohm's Law triangle visually helps students remember the relationship between voltage (V), current (I), and resistance (R):
• Cover the unknown quantity in the triangle.
• The remaining two form the required formula (e.g., V = I × R, I = V / R, or R = V / I).
This aids in quick problem-solving and formula recollection.
11. What is meant by the term ‘potential difference’?
Potential difference is the work done to move a unit charge from one point to another in an electric field. It is measured in volts (V) and is commonly called voltage.
12. How does temperature affect the resistance of a metal conductor?
As temperature increases, the resistance of a metal conductor also increases. This happens because higher temperatures cause more vibration of atoms, hindering the flow of electrons.
