Mains plug 230 V Controller Transformer (step down) Control knob Low voltage Rails Motor Electrical energy (mains) Transformer Electrical energy (low V) Mot...

Fig. 1 shows a model railway controller used at a community exhibition. The controller has a transformer that reduces the 230 V mains potential difference to a safer low potential difference for the track. A train motor receives electrical energy through the rails. A child notices that the train travels faster when the controller setting is raised. The organiser explains that a larger potential difference can cause a larger current in the motor circuit. The controller is kept dry, and the mains plug has a fuse. The diagram shows the mains input, transformer, control knob and rails.

(a) What is the purpose of the transformer in the controller? [1]
(b) Which quantity is measured in volts? [1]
(c) What happens to the motor current when the controller potential difference is increased, assuming its resistance is constant? [2]

A science club investigates how the resistance of a copper wire changes when its length changes. Fig. 1 shows the apparatus: a low-voltage power supply, ammeter, voltmeter, crocodile clips and a metre ruler beside the wire. For each test, the student moves one clip to increase the length of wire in the circuit. The potential difference is kept at 2.0 V. A longer wire gives a smaller current because charge has further to travel through the metal. The student uses the same thickness of copper wire throughout, then draws a graph of resistance against length. The power supply is switched off before the clips are moved.

(a) Which meter is connected in parallel with the test wire? [1]
(b) What equation is used to calculate resistance? [1]
(c) What happens to resistance when the length of the copper wire is increased? [2]