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Ohm’s Law Calculator
Find voltage, current or resistance when the other two are known, with the working shown and the power dissipated. Easy theory on Ohm’s law, resistivity and V–I graphs, guided experiments and a JEE-style solved example are given below the calculator.
🎯 Aim
To apply Ohm’s law, V = IR, and study how current depends on voltage and resistance.
🧰 Apparatus (virtual)
A calculator for V, I or R with step-by-step working and the power dissipated in the resistor.
✅ Outcome
Solve Ohm’s law problems, use R = ρl/A, and read V–I graphs of ohmic and non-ohmic devices.
Theory
What is Ohm’s law?
In 1827 the German physicist Georg Simon Ohm found a simple rule for metal wires: if the temperature and other physical conditions stay the same, the current through a conductor is directly proportional to the potential difference across it. Double the voltage and the current doubles.
Key result
\[ V \propto I \quad\Rightarrow\quad V = I\,R \qquad I = \frac{V}{R} \qquad R = \frac{V}{I} \]A water pipe is a handy picture. The voltage V (in volts) is like the water pressure that pushes, the current I (in amperes) is how much water flows each second, and the resistance R (in ohms, Ω) is how narrow the pipe is. More pressure gives more flow, while a narrower pipe gives less flow.
What decides the resistance?
A wire’s resistance depends on its length l, its cross-sectional area A and the material, described by its resistivity ρ:
Formula
\[ R = \frac{\rho\,l}{A} \qquad\qquad R_T = R_0\left(1 + \alpha\,\Delta T\right) \]A longer wire has more resistance and a thicker wire has less. Copper has a very low resistivity (about 1.7 × 10⁻⁸ Ω·m), which is why it is used for wiring; nichrome has a much higher one, which is why it is used in heaters. For metals, resistance also rises with temperature: α is the temperature coefficient of resistance.
Why does Ohm’s law work? (a peek inside)
Inside a metal, free electrons move about randomly. When a voltage is applied, they slowly drift in one direction with a small drift velocity vd, bumping into ions on the way. The current is I = n e A vd, where n is the number of free electrons per m³. The drift velocity is proportional to the electric field, which is proportional to V, so I is proportional to V. That is Ohm’s law.
Ohmic and non-ohmic devices
| Ohmic | Non-ohmic | |
|---|---|---|
| V–I graph | Straight line through the origin | Curved, or different for each direction |
| Resistance | Constant | Changes with V or I |
| Examples | Metal wires and resistors at constant temperature | Diode, filament bulb, thermistor, LED |
Power in a resistor
A resistor turns electrical energy into heat. Using Ohm’s law, the power can be written in three ways. Pick the one that uses the quantities you know:
Formula
\[ P = V I = I^{2} R = \frac{V^{2}}{R} \]💡 JEE tip
If a wire is stretched to n times its length, its volume stays the same, so its area becomes 1/n times. Then R = ρl/A becomes n² times larger. Also check graph axes carefully: on a V–I graph (V on the y-axis) the slope is R; on an I–V graph (I on the y-axis) the slope is 1/R.
⚠️ Remember
Ohm’s law is not a universal law. It holds only when temperature and other physical conditions stay constant. A glowing bulb filament is much hotter than a cold one, so its resistance while glowing is many times higher than the value a multimeter shows when the bulb is off.
Try it yourself
Guided experiments
Choose what to calculate in step 1, then enter the other two values in step 2. Press Reset between experiments.
Experiment 1
Find the voltage
- Select Voltage (V).
- Enter I = 2 A and R = 6 Ω.
Experiment 2
Double the resistance
- Select Current (I). Enter V = 12 V and R = 6 Ω.
- Then change R to 12 Ω.
Experiment 3
A very small current
- Select Current (I).
- Enter V = 5 V and R = 10000 Ω (10 kΩ).
Experiment 4
Resistance of a glowing bulb
- Select Resistance (R).
- Enter V = 230 V and I = 0.435 A (a 100 W lamp).
Solved example
A nichrome wire, before and after stretching
A nichrome wire is 2 m long, has a cross-sectional area of 0.2 mm² and a resistivity of 1.1 × 10⁻⁶ Ω·m. It is connected across a 22 V supply. Find its resistance, the current and the power. The wire is then stretched uniformly to twice its length and connected to the same supply. Find the new current and power.
- l = 2 m
- A = 0.2 mm²
- ρ = 1.1 × 10⁻⁶ Ω·m
- V = 22 V
Resistance
\[ R = \frac{\rho\,l}{A} = \frac{1.1\times10^{-6}\times2}{0.2\times10^{-6}} = 11\ \Omega \]Current and power
\[ I = \frac{V}{R} = \frac{22}{11} = 2\ \text{A}, \qquad P = V I = 22\times2 = 44\ \text{W} \]After stretching to double length
The volume stays the same, so the area halves. The resistance becomes 2² = 4 times larger:
\[ R' = 4R = 44\ \Omega, \qquad I' = \frac{22}{44} = 0.5\ \text{A}, \qquad P' = 22\times0.5 = 11\ \text{W} \]💡 Check it
Select Current (I) and enter V = 22 V, R = 11 Ω. The calculator gives 2 A and P = 44 W. Change R to 44 Ω to get 0.5 A and P = 11 W. Stretching the wire cut the heater’s power to one quarter.
Where it is used
Applications of Ohm’s law
LED resistors
For a 2 V LED at 20 mA on a 9 V battery: R = (9 − 2) / 0.02 = 350 Ω.
Heaters and fuses
The wire’s resistance sets the current and the heat (P = I²R) it produces.
Multimeters
A meter finds resistance by passing a known current and measuring the voltage.
Sensors
Thermistors and strain gauges change resistance, which a circuit converts into a voltage signal.
Viva voce
Viva questions
Q1State Ohm’s law.
At constant temperature and other physical conditions, the current through a conductor is directly proportional to the potential difference across its ends: V = IR.
Q2Is Ohm’s law a universal law?
No. It applies to metallic conductors at constant temperature. Diodes, transistors, filament lamps, thermistors and electrolytes do not follow it.
Q3What does the slope of a V–I graph give?
With V on the y-axis and I on the x-axis, the slope is the resistance R. If the axes are swapped (I on the y-axis), the slope is 1/R, the conductance.
Q4Why does a bulb’s resistance increase when it glows?
The filament becomes very hot. The metal ions vibrate more strongly, electrons collide with them more often, and the resistivity rises, so the resistance increases.
Q5A wire is stretched to double its length. What happens to its resistance?
Its volume stays the same, so its area halves. Since R = ρl/A, the resistance becomes 2 × 2 = 4 times the original value.
📌 More virtual labs & notes
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