A wire of resistance 'R' is cut into 'n' equal parts. These parts are then connected in parallel with each other. The equivalent resistance of the combination is [[1]].

A wire of resistance

' R'

is cut into

' n'

equal parts. These parts are then connected in parallel with each other. The Equivalent Resistance Formula

of the combination is

\frac{R}{n^{2}}

.
As we know

R \propto l

(length of wire) and we are cutting the wire into n equal segments, then the resistance of each newly wire will be-

= > R_{1} = R_{2} = R_{3} = R_{4} = R_{5} = \dots R_{n} = \frac{R}{n}

Where

R_{1} = First wire resistance; R_{2} = second wire resistance;

R_{3} = third wire resistance; R_{4} = fourth wire resistance;

and

R_{n} = n^{th} wire resistance

. As shown in the diagram, we connect them in parallel, and the equivalent resistance of the combination is given by

R_{eq} .

= > \frac{1}{R_{eq}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} + \frac{1}{R_{4}} + \dots + \frac{1}{R_{n}}

= > \frac{1}{R_{eq}} = \frac{n}{R} + \frac{n}{R} + \frac{n}{R} + \dots + \frac{n}{R^{2}} (n times)

= > \frac{1}{R_{eq}} = (\frac{n}{R}) \times n

= > R_{eq} = \frac{R}{n^{2}}

A wire of resistance $' R'$ is cut into $' n'$ equal parts. These parts are then connected in parallel with each other. The equivalent resistance of the combination is [[1]].