Question

A uniform wire of resistance $R$ and length $L$ is cut into four equal parts, each of length $L/4$, which are then connected in parallel combination. The effective resistance of the combination will be

• A. R
• B. 4R
• C. $\frac{R}{4}$
• D. $\frac{R}{16}$

Answer 1

Answer: (D)

Resistance $R=\frac{pl}{A}$ or $R\propto l$
$\therefore \frac{R_1}{R_2}=\frac{l_1}{l_2}=\frac{L}{L/4}=4$
or $R_2=\frac{R}{4}$ ($\because R_1=R$)
In parallel combination of such four resistances.
$\frac{1}{R^{\prime }}=\frac{1}{R_2}+\frac{1}{R_2}+\frac{1}{R_2}+\frac{1}{R_2}$
or $\frac{1}{R^{\prime }}=\frac{1}{R/4}+\frac{1}{R/4}+\frac{1}{R/4}+\frac{1}{R/4}$
or $\frac{1}{R^{\prime }}=\frac{4}{R}+\frac{4}{R}+\frac{4}{R}+\frac{4}{R}$
or $\frac{1}{R^{\prime }}=\frac{16}{R}$ or $R^{\prime }=\frac{R}{16}$