Question

A coil in the heater consume power P on passing current. If it is cut into halves and joined in parallel, it will consume power:

• A. P
• B. 2P
• C. 4P
• D. 1/2P

Hint:

Cutting a wire into \(n\) equal parts and connecting them in parallel across the same voltage increases the power consumption by a factor of \(n^2\).
Here, \(n = 2\), so the power becomes \(2^2 P = 4P\).

Answer 1

The Correct Option is C

Step 1: Set up variables before cutting.
Say the full coil has resistance \(R\) and is connected to a fixed voltage \(V\), giving power \[ P = \frac{V^2}{R} \]
Step 2: Halve the coil.
Cutting the coil in half cuts its length in half too, and since resistance is proportional to length, each half has resistance \(R/2\).
Step 3: Rejoin in parallel and recompute.
Two equal resistors of \(R/2\) each, joined in parallel, combine as \[ R_{eq} = \frac{R/2}{2} = \frac{R}{4} \] because two identical resistors in parallel simply halve the resistance of one of them.
Step 4: Find the new power.
Feeding the same voltage \(V\) into this smaller resistance gives \[ P' = \frac{V^2}{R/4} = 4\frac{V^2}{R} = 4P \] so the power consumed quadruples.
\[ \boxed{4P} \]