Page 143 - Physics Coursebook 2015 (A level)

Chapter 9: Electric current, potential difference and resistance
Current and charge
When charged particles flow past a point in a circuit, we say that there is a current in the circuit. Electrical current is measured in amperes (A). So how much charge is moving when there is a current of 1 A? Charge is measured in coulombs (C). For a current of 1 A, the rate at which charge passes a point in a circuit is 1C in a time of 1s. Similarly, a current of 2 A gives a charge of 2 C in a time of 1s. A current of 3A gives a charge of 6C in a time of 2s, and so on. The relationship between charge, current and time may be written as the following word equation:
current = charge time
This equation explains what we mean by current.
The equation for current can be rearranged to give an equation for charge:
charge = current × time
This gives us the definition of the unit of charge, the coulomb.
In symbols, the charge flowing past a point is given by the relationship:
∆Q = I∆t
where ∆Q is the charge which flows during a time ∆t and I is the current.
Note that the ampere and the coulomb are both SI units; the ampere is a base unit while the coulomb is a derived unit (see page 40).
WORKED EXAMPLES
1 There is a current of 10 A through a lamp for 1.0 hour. Calculate how much charge flows through the lamp in this time.
Step1 Weneedtofindthetimetinseconds: Δt=60×60=3600s
Step2 WeknowthecurrentI=10A,sothecharge which flows is:
ΔQ=IΔt=10×3600=36000C=3.6×104C
QUESTIONS
3 The current in a circuit is 0.40 A. Calculate the charge that passes a point in the circuit in a period of15s.
4 Calculate the current that gives a charge flow of 150C in a time of 30s.
5 In a circuit, a charge of 50 C passes a point in 20 s. Calculate the current in the circuit.
6 A car battery is labelled ‘50 A h’. This means that it can supply a current of 50 A for one hour.
a For how long could the battery supply a continuous current of 200 A needed to start the car?
b Calculate the charge which flows past a point in the circuit in this time.
Charged particles
As we have seen, current is the flow of charged particles called charge carriers. But how much charge does each particle carry?
Electrons each carry a tiny negative charge of approximately −1.6 × 10−19 C. This charge is represented by −e. The magnitude of the charge is known as the elementary charge. This charge is so tiny that you would need about six million million million electrons – that’s 6000000000000000000 of them – to have a charge equivalent to one coulomb.
elementarycharge e=1.6×10−19C
Protons are positively charged, with a charge +e. This is equal and opposite to that of an electron. Ions carry charges that are multiples of +e and −e.
2 Calculate the current in a circuit when a charge of 180 C passes a point in a circuit in 2.0 minutes.
Electric current is the rate of flow of electric charge past a point.
One coulomb is the charge which flows past a point in a circuit in a time of 1 s when the current is 1 A.
Step1 RearrangingQ=Itgives: I = ∆Q (or current = charge)
∆t time
Step2 Withtimeinseconds,wethenhave:
180 currentI=120 =1.5A
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