Question

The ratio of resistance of two copper wire of the same length and of same cross-sectional area, when connected in series to that when connected in parallel, is

• A. $1:1$
• B. $1:2$
• C. $2:1$
• D. $4:1$
• E. $1:4$

Answer 1

The correct option is D $4:1$

Let $R$ be the resistance of copper wire. In the first condition,
$R_{series}=R+R=2R....\left(i\right)$
In the second condition,
$\frac{1}{R_{parallel}}=\frac{1}{R}+\frac{1}{R}=\frac{1}{R_{parallel}}=\frac{1+1}{R}$
$R_{parallel}=\frac{R}{2}.....\left(ii\right)$

On dividing Eq. (i) by Eq. (ii), we get

$\frac{R_{series}}{R_{parallel}}=\frac{2R}{\frac{R}{2}}=\frac{4}{1}$.