Question

The resistance across $A$ and $B$ in the given figure will be:

• A. None of the above
• B. $3R$
• C. $\frac{R}{3}$
• D. $R$

Answer 1

Answer: (C)

Given: $R_1=R_2=R_3=R$

The three resistances are connected in parallel between the points A and B.

Equivalent resistance for parallel combination:

$\Rightarrow \frac{1}{R_{AB}}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}$

$\Rightarrow \frac{1}{R_{AB}}=\frac{1}{R}+\frac{1}{R}+\frac{1}{R}=\frac{3}{R}$

$\Rightarrow$ $R_{AB}=\frac{R}{3}$