Question

What is the equivalent resistance across A and B?

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

Answer 1

The correct option is C

$\frac{4}{3}\Omega$

The circuit can be converted into

Given $R_1=R_2=R_3=R_4=1\Omega$ and $R_1$, $R_2$ and $R_3$ are in parallel.

When resistors are connected in parallel, equivalent resistance is $\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}$

$\frac{1}{R_{eq}}=\frac{1}{1}+\frac{1}{1}+\frac{1}{1}$

$\Rightarrow \frac{1}{R_{eq}}=3$

$R_{eq}=\frac{1}{3}$

Further, circuit can be deduced to:

Equivalent resistance for this series combination would be $R_{eq}^{\prime }=R_{eq}+R_4=\frac{1}{3}+1=\frac{4}{3}\Omega$

Therefore, equivalent resistance of the given circuit is $\frac{4}{3}\Omega$.