Question

Two conducting wires of the same material and of equal lengths and equal diameters are first connected in series and then parallel in a circuit across the same potential difference. The ratio of equivalent resistance in series and parallel combinations would be:

• A. 1:2
• B. 2:1
• C. 1:4
• D. 4:1

Answer 1

The correct option is C

1:4

Let $R_s$ be the equivalent resistances of the wires if connected in series and $R_p$ be the equivalent resistances of the wires if connected in parallel.
$R_s=R+R=2R$ and $\frac{1}{R_p}=\frac{1}{R}+\frac{1}{R}$
$\frac{1}{R_p}=\frac{2}{R}$ or $R_p=\frac{R}{2}$

Ratio$=\frac{R_s}{R_p}$
$=\frac{2R}{\frac{R}{2}}$
$=\frac{4}{1}$.

Hence, ratio of equivalent resistance in series and parallel combinations is 4:1.