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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:
Original: $$W = \frac{V^2}{R}$$.
Wire cut in two halves: each has resistance $$R/2$$.
Two halves in parallel: $$R_{eq} = \frac{(R/2)(R/2)}{R/2 + R/2} = \frac{R/4}{R} \cdot R = \frac{R}{4}$$.
New power: $$W' = \frac{V^2}{R/4} = \frac{4V^2}{R} = 4W$$.
The answer is Option (4): $$\boxed{4W}$$.
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