The effective resistance of a parallel connection that consists of four wires of equal length, equal area of cross-section and same material is . What will be the effective resistance if they are connected in series? [2021]

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Solution

Q.
The effective resistance of a parallel connection that consists of four wires of equal length, equal area of cross-section and same material is $0.25$ $Ω$ . What will be the effective resistance if they are connected in series [2021]

1 4 $Ω$

2 0.25 $Ω$

3 0.5 $Ω$

4 1 $Ω$

Ans.
(1)

Given that, four wires of same material, equal area of cross-section and equal length.

Resistance of each wire is $' R' .$

For parallel combination, $R_{e q} = 0.25$ $Ω$

When wires are connected in parallel,

$\frac{1}{R_{e q}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} + \frac{1}{R_{4}}$

$\frac{1}{R_{e q}} = \frac{1}{R} + \frac{1}{R} + \frac{1}{R} + \frac{1}{R}$ $;$ $\frac{1}{0.25} = \frac{4}{R} \Rightarrow R = 1$ $Ω$

So, resistance of each wire is $1 Ω$ .

Now, wires are connected in series. Then, equivalent resistance is

$R_{e q} = R_{1} + R_{2} + R_{3} + R_{4}$

$R_{e q} = 1 Ω + 1 Ω + 1 Ω + 1 Ω = 4 Ω$

Hence, the equivalent resistance in series will be $4$ $Ω$ .

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