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

$2:1$

Explanation for the correct solution:

1. When a conductor is cut into half, resistance also decreases to half whereas the resistivity remains same.
2. We have the expression for resistance of the conductor as, $R=\frac{\rho l}{A}$where $\rho$is the resistivity of the material in $\Omega m$, l is the length of the conductor in $m$ and $A$ is the area of a crosssection of the conductor in $m^2$.
3. On cutting half, the new resistance $R^l=\frac{R}{2}$$\Omega$
4. Now, the heat produced by the coil is given by, $H=\frac{V^2}{R}$where $V$ is the potential difference at the ends of the conductor and $R$ is the resistance in ohms.
5. In a household circuit, all the conducting wires are connected in parallel, the potential difference remains the same. Thus, $H\alpha \frac{1}{R}$
6. Hence, the heat produced doubles because the resistance is reduced to half. i.e, $H^l\alpha \frac{1}{R^l}=2\frac{1}{R}=2H$

Hence, the correct option is option A.