If the length of the filament of a heater is reduced by 10%, the power of the heater will

If the length of the filament of a heater is reduced by 10%, the power of the heater will

A
increase by about 9%
B
increase by about 11%
C
decrease by about 11%
D
decrease by about 9%

Solution:

New resistance: $R^{'} = \frac{ρ (0 .9 L)}{A} = 0 .9 R$

$P^{'} = \frac{V^{2}}{R^{'}} = \frac{V}{0 .9 R} = \frac{P}{0 .9}$

Increase in power: $\frac{P^{'} - P}{P} \times 100 = \frac{100}{9} = 11 %$

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