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

Let the original resistance of the heater coil be $$R$$, and let it be connected to a constant voltage supply $$V$$.

The original heat generated per unit time (Power, $$P_1$$) is given by the formula:

$$P_1 = \frac{V^2}{R}$$

When the coil is cut into two equal parts, the length of each part becomes half of the original length ($$L/2$$).

Since the resistance of a wire is directly proportional to its length ($$R \propto L$$), the new resistance of the single half-part ($$R_2$$) will be:

$$R_2 = \frac{R}{2}$$

When this single part is connected to the same voltage supply $$V$$, the new heat generated per unit time ($$P_2$$) is:

$$P_2 = \frac{V^2}{R_2}$$

Substitute the value of $$R_2$$ into the equation:

$$P_2 = \frac{V^2}{\frac{R}{2}}$$

$$P_2 = 2 \left( \frac{V^2}{R} \right)$$

Since $$\frac{V^2}{R}$$ is our initial power $$P_1$$, we get:

$$P_2 = 2 P_1$$

The heat generated will now be doubled.