First slide

Electrical power

Question

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

Moderate

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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