A network of three resistors of resistances R1, R2 and R3 is shown in Fig. 6.1. [Figure 6.1] The individual currents in the resistors are I1, I2 and I3. The total current in the combination of resistors is I and the potential difference across the combination is V. A battery of electromotive force (e.m.f.) 8.0 V and internal resistance r is connected to three resistors X, Y and Z, as shown in Fig. 6.2. [Figure 6.2] Resistor Y has a resistance of 16 Ω. The current in resistor X is 0.49A and the current in resistor Y is 0.45A. Resistors X and Y in Fig. 6.2 are made from wires of the same material and cross-sectional area. The average drift speed of the free electrons in X is 2.1 × 10⁻⁴ m s⁻¹.

1. (a)Show that the combined resistance R of the network is given by 1/R = 1/R₁ + 1/R₂ + 1/R₃[2]
2. (b)(i)Calculate: the current in the battery current = .............................................. A[1]
3. (b)(ii)the internal resistance r of the battery. r = .............................................. Ω[2]
4. (c)Calculate the average drift speed v of the free electrons in Y. v = .............................................. ms⁻¹[2]
5. (d)Resistor Z in Fig. 6.2 is replaced by a new resistor of smaller resistance. State and explain the effect, if any, on the terminal potential difference of the battery.[2]

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