When a potential difference V is applied across a wire of resistance R, it dissipates energy at a rate W. If the wire is cut into two halves and these halves are connected mutually parallel across the same supply, the energy dissipation rate will become:

Solution

Physics sir · 4 steps

Same voltage, so power goes as 1/R: find the new resistance and the rest follows.

1. Start with W. With the full wire across V, the power is W = V²/R.
2. Cut the wire. Resistance is proportional to length, so each half has resistance R/2.
3. Join in parallel. Two equal resistors R/2 in parallel give 1/2 × R/2 = R/4.

   W' = V²/(R/4) = 4 V²/R = 4W

4. So. The resistance drops to a quarter on the same supply, so the energy dissipation rate becomes 4W, option (b).

The idea to keep. When the supply voltage is fixed, use P = V²/R: a smaller resistance means more power. Use P = I²R only when the current is the fixed quantity.

Answer from the NTA final answer key. Solution by PrepWiser.