Question

6. Two metallic wires of the same material are connected in parallel. Wire A
has length land radius r, wire B has a length 21 and radius 2r. Calculate
the ratio of their equivalent resistance in parallel combination and the
resistance of wire A.​

Answer 1

Explanation:

the ratio of {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 R_{p} for the parallel combination must be written as:

\frac{1}{R_{p} it}=\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.