Question

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

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

Answer 1

The correct option is A Doubled

Let $l$ is the original length of the coil and $A$ is the area of the coil.

Thus, the resistance of the coil is $R=\rho \frac{l}{A}$, where $\rho$ is the resistivity of the coil.

Now if the coil is halved then the new length $l^{\prime }=\frac{l}{2}$ but the area of the coil does not change.

So, the resistance of one part of the coil is $R^{\prime }=\rho \frac{l}{2A}=\frac{R}{2}$

The heat generated through the original coil when it is connected to a voltage $V$ is $H=\frac{V^2}{R}\times t$

The heat generated through one part of the coil when it is connected to a voltage $V$ is $H^{\prime }=\frac{V^2}{R^{\prime }}\times t=2\frac{V^2}{R}\times t=2H$

So, the heat generation is doubled.