Question

How many times will the resistance of an identical conductor be increase, if the parallel resistance be change to series one?

Options

• ${\displaystyle \sqrt{n}}$

• ${\displaystyle n}$

• ${\displaystyle n^2}$

• ${\displaystyle n-2}$

Answer 1

${\displaystyle n^2}$

Explanation:

In series combination, effective resistance.

Rs = R + R ................ + n term = ${\displaystyle \frac{n}{R}}$

In parallel combination, effective resistance

${\displaystyle \frac{1}{Rp}=\frac{1}{R}+\frac{1}{R}}$ + .............. n term = ${\displaystyle \frac{n}{R}}$

RP = ${\displaystyle \frac{R}{n}}$

${\displaystyle \frac{Rs}{Rp}=\frac{nR}{\frac{R}{n}}=n^2}$