Question

Two metallic wires A and B are connected in parallel . Wire A has length l and radius r, wire B has a length 2l and radius 2r , Compute the ratio of the total resistance of parallel combination and the resistance of wire A.

Answer 1

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Answer 2

The ratio of $\bold{R_{p} \text { and } R_{A} \text { is } 1 : 3}$

Given:

Wire A:  

Length = l  

Radius = r

Wire B;

Length = 2l

Radius = 2r  

Resistance of $A : R_{A}=\frac{\rho \times l}{\pi r^{2}}$

Resistance of $B : R_{B}=\frac{\rho \times 2 l}{\pi\left(2 r^{2}\right) \times 2}$    

The resistance $R_{p}$ for the parallel combination must be written as:

$\frac{1}{R_{p}}=\frac{1}{R_{A}}+\frac{1}{R_{B}}=\frac{\pi r^{2}}{\rho \times l}+\frac{2 \pi r^{2}}{\rho \times l}$

$R_{p}=\frac{\rho \times l}{3 \pi r^{2}}$

Hence the ratio of $R_{p} \text { and } R_{A}$ will be 1 : 3.