Question

If the length of 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. increase by about 19%
• D. increase by about 10%

Answer 1

The correct option is D increase by about 10%

$P=\frac{V^2}{R}R=\frac{\rho l}{A}\therefore P=\frac{V^{2}A}{\rho l}$

$\therefore P\alpha \frac{1}{l}$ [Keep in $\frac{v^{2}A}{\rho }$ constant]

$\therefore$ with reduction of $l$ by $10\%$ power will increase by $10\%$.