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Ohm's Law and Electric Circuits
Electromagnetism
Ohm's law is the starting point for almost all circuit analysis. It links the voltage across a component, the current through it, and its resistance in one simple equation.
What Ohm's law says
Ohm's law states that the current through a conductor is directly proportional to the voltage across it, provided the temperature stays constant. The constant of proportionality is the resistance, measured in ohms, symbol Omega. A larger resistance means less current for the same voltage, just as a narrower pipe carries less water for the same pressure. Many metals obey Ohm's law well at constant temperature, and they are called ohmic conductors. Devices such as filament lamps and diodes are non-ohmic: their resistance changes with voltage or temperature, so the current-voltage graph is a curve rather than a straight line through the origin.
Series and parallel circuits
In a series circuit there is only one path for the current, so the same current flows through every component and the voltages add up to the supply voltage. The total resistance is the sum of the individual resistances. In a parallel circuit each component connects directly across the supply, so each gets the full voltage, the currents add up, and the total resistance is less than the smallest single resistance. Household wiring is parallel so that each appliance gets the full mains voltage and can be switched off independently. A short circuit is a very low resistance path that draws a dangerously large current, which is why fuses and circuit breakers are fitted.
Where you see it
Ohm's law is used every time an engineer chooses a resistor to limit the current through an LED, sizes a fuse, or checks why a phone charger gets warm. Electric heaters, kettles and toasters turn electrical energy into heat in a resistor, and their power depends on voltage and resistance. Dimmer switches, volume controls and sensor circuits all rely on changing resistance to change current. Even a simple torch is an Ohm's law circuit: a battery, a switch, a bulb with a certain resistance, and the current that makes the filament glow.
Worked example: current and power in a resistor
A 12 V battery is connected across a 4.0 ohm resistor. Find the current: I = V / R = 12 / 4.0 = 3.0 A. Find the power: P = V I = 12 x 3.0 = 36 W. Check with the other form: P = I^2 R = (3.0)^2 x 4.0 = 9.0 x 4.0 = 36 W. Both agree. So 3.0 A flows and 36 W is turned into heat in the resistor. If the resistor were doubled to 8.0 ohms, the current would halve to 1.5 A and the power would fall to 18 W.
Common mistakes
- Using V = IR with the wrong voltage: use the voltage across that one component, not the whole supply voltage, unless it is the only component.
- Mixing up series and parallel resistance: resistances add in series, but in parallel the reciprocal of the total is the sum of the reciprocals.
- Forgetting units: current in amperes, resistance in ohms and voltage in volts must be used together; milliamps must be converted to amps first.
Practice questions
- A 9.0 V battery drives 0.50 A through a resistor. What is the resistance?
Show answer
R = V/I = 9.0 / 0.50 = 18 ohms.
- A 240 V kettle draws 10 A. What power does it use?
Show answer
P = VI = 240 x 10 = 2400 W = 2.4 kW.
- Two 6.0 ohm resistors in series are connected to 12 V. What is the current?
Show answer
Total R = 12 ohms, so I = 12/12 = 1.0 A.
Frequently asked questions
Does Ohm's law apply to all components?
No. It applies to ohmic conductors at constant temperature; lamps, diodes and transistors are non-ohmic.
Why does a resistor get hot?
Moving charges collide with atoms in the resistor, transferring electrical energy into thermal energy at the rate P = I^2 R.