Electric current
Electric current is the rate of flow of electric charge through a conductor.
I = Q / t
Charge Q is measured in coulombs (C), time t in seconds, and current I in amperes (A). One ampere is a flow of one coulomb per second. Current is measured with an ammeter, which is always connected in series.
In a metal wire the charge carriers are electrons. By convention, the direction of current is taken as the direction positive charge would flow, which is opposite to the direction of electron flow.
Potential difference
Charges flow only when there is a potential difference (p.d.) between two points, much as water flows only when there is a difference in height. The p.d. between two points is the work done to move a unit charge from one point to the other:
V = W / Q
It is measured in volts (V) with a voltmeter, which is connected in parallel across the component. A cell or battery maintains the potential difference in a circuit.
Ohm's law
For a metallic conductor at constant temperature, the current through it is directly proportional to the potential difference across it:
V = I R
The constant R is the resistance, measured in ohms (Ω). A graph of V against I for such a conductor is a straight line through the origin.
Example. A bulb draws 0.5 A from a 220 V supply. What is its resistance?
R = V / I = 220 / 0.5 = 440 Ω.
What decides resistance?
The resistance of a wire depends on:
its length l: doubling the length doubles R,
its area of cross-section A: doubling the area halves R,
the material, through a constant called resistivity ρ (rho),
temperature: for metals, resistance increases as temperature rises.
R = ρ l / A
Resistivity is measured in ohm-metre (Ω m). Metals such as copper and aluminium have low resistivity and are used for wires. Alloys such as nichrome have high resistivity and do not oxidise easily, so they are used in heating elements.
Resistors in series and in parallel
Series | Parallel | |
|---|---|---|
Arrangement | End to end, one path | Side by side, separate paths |
Current | Same through each resistor | Divides between branches |
Potential difference | Divides between resistors | Same across each resistor |
Equivalent resistance | R = R₁ + R₂ + R₃ | 1/R = 1/R₁ + 1/R₂ + 1/R₃ |
In series the total resistance is larger than the largest resistor. In parallel it is smaller than the smallest resistor.
Example. Two resistors of 6 Ω and 3 Ω are connected in parallel. Find the equivalent resistance.
1/R = 1/6 + 1/3 = 1/6 + 2/6 = 3/6, so R = 2 Ω.
Household wiring is done in parallel. Every appliance then gets the full mains voltage, each can be switched on and off independently, and one faulty appliance does not cut off the others.
Heating effect of current
When current flows through a resistor, electrical energy is converted into heat. The heat produced in time t is given by Joule's law of heating:
H = I² R t
This effect is used in electric irons, toasters, heaters, bulb filaments (which glow white-hot) and fuses. A fuse wire melts when the current exceeds a safe value, breaking the circuit.
Electric power and energy
Power is the rate at which electrical energy is used:
P = V I = I² R = V² / R
Power is measured in watts (W). Electricity bills charge for energy, measured in kilowatt-hours:
1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ J. This is the "unit" on your bill.
Example. A 1500 W geyser runs for 2 hours a day. How many units does it use in 30 days?
Energy = 1.5 kW × 2 h × 30 = 90 kWh, so 90 units.
Quick summary
I = Q/t, V = W/Q, V = IR.
R = ρl/A: longer wire means more resistance, thicker wire means less.
Series resistances add; in parallel, add the reciprocals.
H = I²Rt, P = VI, and 1 kWh = 3.6 × 10⁶ J.