Question

The equivalent resistance between points $A$ and $B$ is.

• A. $2R$
• B. $\frac{3}{4}R$
• C. $\frac{4}{3}R$
• D. $\frac{3}{5}R$

Answer 1

The correct option is D $\frac{3}{5}R$

Formula for equivalent resistance in series

$R=R_1+R_2$

Formula for equivalent resistance in parallel

$\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}$

Now, given circuit can be rearrange as in figure 2

Using formula for equivalent resistance in parallel

$\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}$

Equivalent resistance beween B and C $=\frac{R}{2}$

and it is in series with resistance(AC), So resistance of lower branch $=\frac{3R}{2}$

Now, equivalent resistance between A and B

$\frac{1}{R_{eq}}=\frac{1}{R}+\frac{2}{3R}$

$\Rightarrow R_{eq}=\frac{3R}{5}$

Therefore, D is correct option.