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A transformer is used to light a 100 W and 110 V lamp from a 220 V mains. If the main current is 0.5 amp, the efficiency of the transformer is approximately
A
50%
B
90%
C
10%
D
30%
Detailed Solution
Efficiency of the transformer: $\eta = \dfrac{P_{output}}{P_{input}} \times 100$
Output power = power of the lamp = 100 W
Input power $= V_p I_p = 220 \times 0.5 = 110$ W
$\eta = \dfrac{100}{220 \times 0.5} \times 100 = \dfrac{100}{110} \times 100$
$\eta = 90.9$ percent
So the efficiency is approximately 90%.
Output power = power of the lamp = 100 W
Input power $= V_p I_p = 220 \times 0.5 = 110$ W
$\eta = \dfrac{100}{220 \times 0.5} \times 100 = \dfrac{100}{110} \times 100$
$\eta = 90.9$ percent
So the efficiency is approximately 90%.