Current Electricity

JEE Main level, single correct, medium

85 of 380

Question 85 of 380

The resistance of a wire is RR. It is bent at the middle by 180∘180^{\circ} and both the ends are twisted together to make a shorter wire. The resistance of the new wire is

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Answer: (C) R/4R / 4

Resistance of wire (R)=ρlA(R)=\rho \frac{l}{A} If wire is bent in the middle then
l′=l2,A′=2 A∴ New resistance, R′=ρl′A′=ρl22A=ρl4A=R4. \begin{aligned} & l^{\prime}=\frac{l}{2}, A^{\prime}=2 \mathrm{~A} \\ & \therefore \text { New resistance, } \mathrm{R}^{\prime}=\rho \frac{l^{\prime}}{\mathrm{A}^{\prime}} \\ & =\frac{\rho \frac{l}{2}}{2 A}=\frac{\rho l}{4 A}=\frac{R}{4} \text {. } \\ & \end{aligned}

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