## Question

A circuit consists of three resistors, R_{1}, R_{2} and R_{3}, and two switches A and B, as shown in the figure.

The resistances between terminals X and Y is measured for different settings of the switches A and B. The results are shown in the table.

a) Determine the resistance of resistors R_{1}, R_{2} and R_{3}.

b) Switch A is now closed and switch B is open. Calculate the resistance between terminals X and Z.

## Answer

a) From the first row in the table, when switches A and B are both open, the total resistance is 12Ω.

Assuming that X is positive and Y is negative, current will flow through the circuit as shown.

Hence, we see that:

From the second row in the table, when switch A is open and B is closed, the total resistance is 10Ω.

Assuming that X is positive and Y is negative, current will flow through the circuit as shown.

Hence, we see that:

From the third row in the table, when switch A is closed and B is open, the total resistance is 6Ω.

Assuming that X is positive and Y is negative, current will flow through the circuit as shown.

Hence, we see that:

Solving the equations:

we obtain

R2 = 4 Ω

R3 = 2 Ω

b) When switch A is closed and B is open, we need to find the total resistance between X and Z.

Assuming that X is positive and Z is negative, current will flow through the circuit as shown.