A wire of resistance R and length L is cut into 5 equal parts. If these parts are joined parallely, then resultant resistance will be :

Question

Quantrex Academy · Accepted Answer

Correct answer: A. (R)/(25)

Resistance of each part will be equally divided. So, the resistance of each part of the wire can be expressed as $\dfrac{R}{5}$ .

The formula to calculate the equivalent resistance of the combination of resistors is given by

$\dfrac{1}{{R}_{eq}} = \mathop{∑}_{i = 1}^{5}\dfrac{1}{{R}_{i}} . . . \left(1\right)$

From equation (1), it follows that

$\dfrac{1}{{R}_{eq}} = \dfrac{5}{R} + \dfrac{5}{R} + \dfrac{5}{R} + \dfrac{5}{R} + \dfrac{5}{R} = \dfrac{25}{R} ⇒ {R}_{eq} = \dfrac{R}{25}$

A wire of resistance R and length L is cut into 5 equal parts. If...