Heater Coil Cutting – Rankers Physics

Power of Electrical Circuit: Practice Problem & Solution

Assertion (A): The coil of a heater is cut into two equal halves and only one of them is used into heater. The heater will now require half the time to produce the same amount of heat. Reason (R): The heat produced is directly proportional to the square of current.  
(1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
(2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(3) (A) is true but (R) is false
(4) Both (A) and (R) are false

Solution Explained:

To solve this problem, we apply the core principles of Power of Electrical Circuit. Understanding the underlying formula is key to arriving at the correct answer below:

When the heater coil is cut in half, its resistance becomes \( R' = R/2 \). Since \( H = \frac{V^2}{R}t \), for the same heat \( H \) and constant voltage \( V \), the time \( t \) is proportional to \( R \). Halving \( R \) halves \( t \). So (A) is true. (R) is also true by Joule's law, but it does not explain (A) because (A) implicitly assumes constant voltage, where \( I \) would change.

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