Question

Calculate the equivalent resistance between $A$ and $B$ from the following diagram;

• A. $5\Omega$
• B. $3\Omega$
• C. $4\Omega$
• D. $9\Omega$

Answer 1

The correct option is B $3\Omega$

$\text{Step 1: Combining series resistances}$

From Fig. 1

$R_1$ and $R_2$ are in series

$R_a=R_1+R_2=3+2=5\Omega$

$R_4$ and $R_5$ are in series

$R_b=R_4+R_5=6+4=10\Omega$

$\text{Step 2: Combining parallel resistances}$

From Fig. 2

$R_a,R_3,R_b$ are in parallel.

$\frac{1}{R_{eq}}=\frac{1}{R_a}+\frac{1}{R_3}+\frac{1}{R_b}$

$\Rightarrow \frac{1}{R_{eq}}=\frac{1}{5}+\frac{1}{30}+\frac{1}{10}$

$\Rightarrow R_{eq}=\frac{30}{10}=3\Omega$

Hence Option B is correct,