In the circuit shown, lamp P is rated 250 V, 50 W and lamp Q is rated 250 V, 200 W. The two lamps are connected in series to a 250 V power supply.

Question 3

In the circuit shown, lamp P is rated 250 V, 50 W and lamp Q is rated 250 V, 200 W. The two lamps are connected in series to a 250 V power supply.

Assume that the resistance of each lamp remains constant.

Which statement most accurately describes what happens when the switch is closed?

A Lamp P emits four times as much power as lamp Q.

B Lamp P emits twice as much power as lamp Q.

C Lamp Q emits four times as much power as lamp P.

D Lamp Q emits twice as much power as lamp P.

Reference: Past Exam Paper – November 2015 Paper 13 Q34

Solution:

Answer: A.

Lamp P is rated 250 V, 50 W.

Lamp Q is rated 250 V, 200 W.

Power P = VI = I²R = V² / R

We need to find the resistance of each lamp. Since we do not know the current we have to use the formula

P = V² / R

to calculate the resistances from the ratings.

Resistance R = V² / P

Lamp P: Resistance = 250² / 50 = 1250 Ω

Lamp Q: Resistance = 250² / 200 = 312.5 Ω

Lamp P and Q are connected in series so, the same current flows through them.

Power emitted = VI

Since current I is the same for both lamps, we can conclude that the power emitted is proportional to the p.d. across the lamp.

Power emitted by lamp P: P_P ∝ 1250

Power emitted by lamp Q: P_Q ∝ 321.5

 

Since the resistance of lamp P is (1250 / 312.5 =) 4 times that of lamp Q, the power emitted by lamp P is also 4 times as much as the power emitted by lamp Q.