Question

The coil of a heater is cut into two equal halves and only one of them is used in the heater. The ratio of the heat produced by this half of the coil to that produced by the original coil is:

• A. 2:1
• B. 4:1
• C. 1:2
• D. 1:4

Answer 1

The correct option is A 2:1

We know that $R=\rho \frac{L}{A}$

Hence, on cutting half $R^{\prime }=\frac{R}{2}$

And for same end potential difference as in house hold circuits-

$H=\frac{V^2}{R}$

$⟹H\propto \frac{1}{R}$

$⟹\frac{H^{\prime }}{H}=\frac{R}{R^{\prime }}=2$

Answer-(A)