Extract:
A cylindrical metal wire W1, of length L and cross-sectional area A, has a resistance of 16 Ω. A second cylindrical wire W2, of length L/2 and cross-sectional area 2A, is made from the same metal.
(i) the resistance of W2: R_2 = 4 Ω
(ii) the effective resistance of W1 and W2 when connected in parallel: resistance of parallel pair = 3.2 Ω
Recall the equation for resistors in parallel:
1/R = 1/R_1 + 1/R_2
W1 and W2 are connected in parallel.
Extended tier only
The parallel pair of resistors in (b)(ii) is connected to a battery that is made from three cells in series, each of electromotive force (e.m.f.) E. There is a current in each resistor.
(i) State the e.m.f. of the battery.
(ii) The current in the battery is IB, the current in W1 is I1 and the current in W2 is I2.
Place a tick in one box to indicate how these three currents are related.
square I1 > I2 > IB
square I1 > IB > I2
square I2 > I1 > IB
square I2 > IB > I1
square IB > I1 > I2
square IB > I2 > I1
square I1 = I2 = IB