Question

Find equivalent resistance between A & B in the circuit:

• A. 18
• B. 8.5
• C. 16.5
• D. 49

Answer 1

The correct option is C

16.5

In the given circuit, the series combination of $12\Omega \&18\Omega$ is in parallel with the resistor of resistance $10\Omega$.

The equivalent resistance of the series combination is given by
$R_{eq}=(12\Omega +18\Omega )=30\Omega .$

Now this $30\Omega$ and $10\Omega$ are in a parallel combination,
We know that the equivalent resistance for a parallel combination of resistors is given by:
$\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+........+\frac{1}{R_n}$

$\therefore ,\frac{1}{R_{eq}}=\frac{1}{30}$$+\frac{1}{10}=\left(\frac{1+3}{30}\right)$
$\frac{1}{R_{eq}}=\frac{4}{30}$
$R_{eq}=\frac{30}{4}=7.5\Omega$

Now $9\Omega \&7.5\Omega$ are in series.
$\therefore R_{eq}=9+7.5=16.5\Omega$ which is the equivalent resistance between the terminals A and B.