(a) Define electric potential difference (p.d.). (b) A wire of cross-sectional area A is made from metal of resistivity ρ. The wire is extended. Assume that the volume V of the wire remains constant as it extends. Show that the resistance R of the extending wire is inversely proportional to A². (c) A battery of electromotive force (e.m.f.) E and internal resistance r is connected to a variable resistor of resistance R, as shown in Fig. 6.1. [Figure 6.1] The current in the circuit is I. Use Kirchhoff's second law to show that R = (E/I) - r. (d) An ammeter is used in the circuit in (c) to measure the current I as resistance R is varied. Fig. 6.2 is a graph of R against 1/I. [Figure 6.2]

1. (a)Define electric potential difference (p.d.). [1][1]
2. (b)Show that the resistance R of the extending wire is inversely proportional to A². [2][2]
3. (c)Use Kirchhoff's second law to show that R = (E/I) - r. [1][1]
4. (d)(i)Use Fig. 6.2 to determine the power dissipated in the variable resistor when there is a current of 2.0 A in the circuit. power = ........................................................... W [3][3]
5. (d)(ii)1.state the internal resistance r of the battery r = ................................................................ Ω[1]
6. (d)(ii)2.determine the e.m.f. E of the battery. E = ................................................................ V [3][3]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.