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Sunday, November 25, 2018

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: PP 1250
Power emitted by lamp Q: PQ 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.

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