Question

A heater coil is cut into two equal parts and only one part is used in the heater. Then the heat generated becomes:

• A. One fourth
• B. Half
• C. Double
• D. Four times

Answer 1

Answer: (C)

Double

Resistance $R=\frac{\rho l}{A}$

When resistance has cut into two equal parts then its length will become half but area of crosssection will not change.

ie;

$l^{\prime }=\frac{l}{2}{A}^{\prime }=A$

New resistance $R^{\prime }=\frac{\rho l^{\prime }}{A^{\prime }}=\frac{R}{2}$

Heat generated $H$$=\frac{V^2}{R}t$
And

$\Rightarrow$ $H^{\prime }=\frac{V^2}{R^{\prime }}t$

On Putting value of R'

$H^{\prime }=2\times \frac{V^2}{R}t$

$H^{\prime }=2H$

Option C.