Question

A uniform conducting wire offers a resistance of 60 Ω. It is cut into 12 equal parts and 6 of them are connected in parallel and remaining 6 are connected in series. This parallel bundle is connected in series with the series chain. Then, find the net resistance.

• A. 30.84 Ω
• B. 32.84 Ω
• C. 29.84 Ω
• D. 31.84 Ω

Answer 1

The correct option is A

30.84 Ω

Resistance of complete wire = $60\Omega$
Resistance of each part = $\frac{60}{12}=5\Omega$
Net resistance of 6 resistances, having $5\Omega$ each, in parallel $R_p=\frac{5}{6}\Omega$
Net resistance of 6 resistances, having $5\Omega$ each, in series $R_s=30\Omega$

Thus, effective resistance $R_{eff}$ of parallel bundle $R_p$ connected in series with the series chain $R_s$
$R_{eff}=R_p+R_s$

$R_{eff}=\frac{5}{6}\Omega +30\Omega$

$=\frac{185}{6}\Omega =30.84\Omega$