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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