Question

If the length of the filament of a heater is cut by $10\%$ and removed, the power of the heater will

• A. Increase by about $9\%$
• B. Increase by about $11\%$
• C. Increase by about $9\%$
• D. Decrease by about $10\%$

Answer 1

The correct option is B Increase by about $11\%$

We know that
$R=\frac{\rho l}{A}$.......(i)
When the length is cut by $10\%$....(ii)
$R^{\prime }=\frac{\rho \times 0.9l}{A}$
Power (P) = $\frac{V^2}{R}$....(iii)

Similarly,
$P^{\prime }=\frac{V^2}{R^{\prime }}$....(iv)

Change in power is given by
$\Delta P$ = $\frac{P^{\prime }-P}{P}\times 100$...(v)

Using (i), (ii), (iii) and (iv) in (v) we get
$\Delta P$ = $11\%$ (increase)