Current Electricity

JEE Main level, single correct, medium

235 of 380

Question 235 of 380

When a potential difference VV is applied across a wire of resistance RR, it dissipates energy at a rate W.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:

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Answer: (D) 4W4W

For first case:
V2R=W\dfrac{{V}^{2}}{R}=W ...(i)
Now, equivalent resistance of the combination will be R2×R2R2+R2=R4\dfrac{\dfrac{R}{2}\times \dfrac{R}{2}}{\dfrac{R}{2}+\dfrac{R}{2}}=\dfrac{R}{4}
For second case:
W′=V2R4{W}^{'}=\dfrac{{V}^{2}}{\dfrac{R}{4}} ...(ii)
From (i) & (ii), we get
W′=4W{W}^{'}=4W

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