Question

When 'n' wires which are identical are connected in series, the effective resistance exceeds that when they are in parallel by X/Y $\Omega$. Then the resistance of each wire is

• A. $\frac{xn}{y{(n}^2-1)}$
• B. $\frac{yn}{x{(n}^2-1)}$
• C. $\frac{xn}{y(n-1)}$
• D. $\frac{yn}{x(n-1)}$

Answer 1

The correct option is A $\frac{xn}{y{(n}^2-1)}$

Let the resistance of each wire is R

n identical wires of resistance R is connected in series combination,

so, Req = R + R + R + R + .... n times

Req = nR

Similarly, n same identical wires of resistance R is connected in parallel combination,

so, $\frac{1}{Req}=\frac{1}{R}+\frac{1}{R}+\frac{1}{R}$ .......n times

Req = $\frac{R}{n}$

Given, Equivalent resistance in series - equivalent resistance in parallel

=$\frac{X}{Y}\Omega$

so, nR - $\frac{R}{n}=\frac{X}{Y}$

=$R(n^2-1)/n=\frac{X}{Y}$

$R=nX(n^2-1)Y\Omega$