Question

A heater coil is cut into two equal parts and only one part is used in the heater. The heat generated now will be

• A. Doubled
• B. Four times
• C. One fourth
• D. Halved

Answer 1

The correct option is A Doubled

$\text{Step 1: Initial Heat generated}$

$H=\frac{V^{2}t}{R}$
$\text{Step 2: When the coil is cut, new resistance}$

We know that, Resistance $R=\rho \frac{\ell }{A}$

i.e. $R\propto \ell$

Since, the length becomes half, ${\ell }^{\prime }=\frac{\ell }{2}$

$\therefore R^{\prime }=\frac{R}{2}$

$\text{Step 3: Final Heat generated}$

As the supply is same, hence voltage will remain same.
So, $H^{\prime }=\frac{V^2}{R^{\prime }}t$

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

Hence, heat generated will be doubled.

Therefore Option (A) is correct.