Question

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 $9\%$

Answer 1

Answer: (B)

New resistance: $R^{\prime }=\frac{\rho (0.9L)}{A}=0.9R$
$P^{\prime }=\frac{V^2}{R^{\prime }}=\frac{V^2}{0.9R}=\frac{P}{0.9}$
Increase in power: $\frac{P^{\prime }-P}{P}\times 100$
$=\frac{100}{9}=11\%$