Electric current, potential difference and circuit symbols
Current is the rate of flow of charge (I = Q/t). Potential difference is the work done per unit charge (V = W/Q) that drives the charge round a circuit.
Current and potential difference
Electric current is the amount of charge flowing through a cross-section of a conductor in unit time: I = Q/t. In metal wires, the moving charges are electrons. A continuous, closed path for the current is an electric circuit. If the path breaks, for example when a switch is turned off, the current stops. By convention, the direction of current is the direction in which positive charge would flow, so it is opposite to the flow of electrons. Charge flows only when there is a potential difference across the conductor, just as water flows from high pressure to low pressure. A cell or battery makes this potential difference by chemical action inside it. The potential difference between two points is the work done to move a unit charge from one point to the other: V = W/Q.
Units and meters to remember
- 1 ampere is 1 coulomb of charge flowing through a cross-section in 1 second.
- Small currents: 1 mA (milliampere) = 10⁻³ A; 1 μA (microampere) = 10⁻⁶ A.
- 1 coulomb is the charge of nearly 6 × 10¹⁸ electrons.
- 1 volt is the potential difference when 1 joule of work moves 1 coulomb of charge between two points.
- An ammeter measures current. It is joined in series, so all the current passes through it.
- A voltmeter measures potential difference. It is joined in parallel, across the two points.
Circuit symbols you must draw
| Component | How to draw the symbol | What it does |
|---|---|---|
| Electric cell | A long thin line (+) and a short thick line (−), side by side | Gives a potential difference |
| Battery | Two or more cell symbols joined in a row | Gives a larger potential difference |
| Plug key or switch (open) | Two small brackets ( ) on the wire with an empty gap | Circuit is broken: OFF |
| Plug key or switch (closed) | The same brackets with a dot (•) between them | Circuit is complete: ON |
| Wire joint | Two wires meeting, with a dark dot at the joint | Connects the wires |
| Wires crossing without joining | One wire drawn across the other with no dot | No connection |
| Electric bulb | A circle with a cross inside it | Gives light |
| Resistor of resistance R | A zigzag line | Opposes the current |
| Variable resistance (rheostat) | A zigzag line with an arrow drawn across it | Changes the current |
| Ammeter | A circle with A inside, + and − marked | Measures current |
| Voltmeter | A circle with V inside, + and − marked | Measures potential difference |
Worked example: charge and electrons
A current of 0.4 A flows through a torch bulb for 5 minutes. (a) How much charge flows through it? (b) How many electrons pass through the bulb each second? (Charge of an electron = 1.6 × 10⁻¹⁹ C)
- Given: I = 0.4 A, t = 5 min = 5 × 60 s = 300 s.
- (a) Formula: Q = I × t.
- Q = 0.4 A × 300 s = 120 C.
- (b) Charge passing in 1 s = 0.4 A × 1 s = 0.4 C.
- Number of electrons n = Q/e = 0.4 C ÷ (1.6 × 10⁻¹⁹ C).
- n = 0.25 × 10¹⁹ = 2.5 × 10¹⁸.
(a) 120 C; (b) 2.5 × 10¹⁸ electrons per second
Worked example: potential difference
12 J of work is done to move 2 C of charge from one end of a wire to the other. Find the potential difference across the wire. How much work is needed to move 5 C across the same wire?
- Given: W = 12 J, Q = 2 C.
- Formula: V = W/Q.
- V = 12 J ÷ 2 C = 6 V.
- For 5 C: W = V × Q = 6 V × 5 C = 30 J.
Potential difference = 6 V; work for 5 C = 30 J
A mobile charger label reads something like 5 V, 2 A: the volts are the push and the amperes are the flow. A torch cell gives 1.5 V, while the supply in Indian homes is 220 V.
1 marks: “Name the device used to measure potential difference and state how it is connected in a circuit.” A voltmeter, connected in parallel across the two points.
2 marks: “Define 1 volt. How much work is done in moving 4 C of charge across a potential difference of 9 V?” 1 V is the potential difference when 1 J of work moves 1 C of charge. W = VQ = 9 V × 4 C = 36 J.
3 marks: “Draw the symbols of a cell, a battery, a closed plug key, an ammeter, a voltmeter and a rheostat.” Six neat symbols, half a mark each: long and short lines; several cells in a row; brackets with a dot; A in a circle; V in a circle; zigzag with an arrow across it.
I = Q/t counts coulombs per second; V = W/Q counts joules per coulomb. Ammeter goes in line (series), voltmeter goes alongside (parallel).