Current Electricity

JEE Main level, single correct, medium

54 of 380

Question 54 of 380

A wire of resistance RR and length LL is cut into 55 equal parts. If these parts are joined parallely, then resultant resistance will be :

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Answer: (A) R25\dfrac{R}{25}

Resistance of each part will be equally divided. So, the resistance of each part of the wire can be expressed as R5\dfrac{R}{5}.
The formula to calculate the equivalent resistance of the combination of resistors is given by
1Req=∑i=151Ri...(1)\dfrac{1}{{R}_{eq}}=\sum _{i=1}^{5}\dfrac{1}{{R}_{i}}...\left(1\right)
From equation (1), it follows that
1Req=5R+5R+5R+5R+5R=25R⇒Req=R25\dfrac{1}{{R}_{eq}}=\dfrac{5}{R}+\dfrac{5}{R}+\dfrac{5}{R}+\dfrac{5}{R}+\dfrac{5}{R} =\dfrac{25}{R} \Rightarrow {R}_{eq}=\dfrac{R}{25}

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