A wire is cut into three equal parts and then connected in parallel with the same source.

(a) How will its Resistance and Resistivity get affected?

(b) How would the total current and the current through the parts change?

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Solution

(a) Let Resistance of a wire = R $Ω$

When cut into 3 equal parts

Resistance of each part= $\frac{R}{3} Ω$

When connected in Parallel, net resistance $R_{p}$ is given by,

$\frac{1}{R_{p}} = \frac{1}{(R / 3)} + \frac{1}{(R / 3)} + \frac{1}{(R / 3)} \frac{1}{R_{p}} = \frac{9}{R} R_{p} = \frac{R}{9}$

Resistivity will remain same.

(b) Current through each part will be triple the previous and total current in the circuit will be 9 times.

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A wire is cut into three equal parts and then connected in parallel with the same source. (a) How will its Resistance and Resistivity get affected? (b) How would the total current and the current through the parts change?

A wire is cut into three equal parts and then connected in parallel with the same source.

(a) How will its Resistance and Resistivity get affected?

(b) How would the total current and the current through the parts change?