A combination of resistors shown below represents a pair of transmission lines with a fault in the insulation between them. The wires have a uniform resistance, but do not have the same resistance as each other. The following procedure is used to find the value of the resistance R5.
[Figure: Circuit diagram showing resistors R1, R2, R3, R4 in a rectangle with R5 connecting the middle points, terminals labeled A, C, B, D]
A potential difference of 1.5 V is connected in turn across various points in the arrangement.
- With 1.5 V applied across terminals AC a current of 37.5 mA flows
- With 1.5 V applied across terminals BD a current of 25 mA flows
- With 1.5 V applied across terminals AB a current of 30 mA flows
- With 1.5 V applied across terminals CD a current of 15 mA flows
a) Write down four equations relating the potential difference, the resistor values and the currents. [4]
b) Determine the value of resistor R5. [2]
c) If the ends C and D are connected together, what would be the resistance measured between A and B? [3]
d) If the length AC (and also BD) is 60 metres of resistive wire, how far from A (or C) does the fault occur? [2]