The diagram below shows three identical resistors and a battery that supplies a constant 12 V. With the switch open, as shown, the current in resistor Y is 20 mA. When the switch is closed, what is the current in resistor X, and what is the potential difference (voltage) across resistor Z

Answer:

20) F

Since the switch is now closed, current is likely to flow through the wire with the switch rather than through resistor Y. Current always flows where there is least resistance.
Current in Y = 0
Hence voltage in Y = 0
Now voltage is shared amongst two resistors (X and Z) instead of three.
Since X and Z are identical resistors, they would have the same resistance as well.

Voltage in Z = 12 ÷ 2 = 6V

Voltage in Y when switch was open = 12 ÷ 3 = 4V
Current in Y when switch was open (given) = 20mA = 0.02A
Resistance in Y when switch was open = V/I = 4 ÷ (0.02) = 200Ω

Each resistor therefore has a resistance of 200Ω
When the switch is closed, there are two resistors. Hence total resistance = 200 x 2 = 400Ω
When switch is closed, Current = 12 ÷ 400 = 0.03 A = 30mA

Hence F is the answer.