Question

Find equivalent resistance between A & B in the circuit:

• A. 16.5

Answer 1

The correct option is A 16.5
Since $12\Omega \&18\Omega$ are in series.
We know for series connection,
$R_{eq}=R_1+R_2+R_3+...+R_n$
we can substitute the values,
$(12\Omega +18\Omega )$ as $30\Omega .$
Now, $30\Omega \&10\Omega$ are in parallel & we know,
For parallel,
$\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...+\frac{1}{R_n}$
$\therefore \frac{1}{R}=\frac{1}{30}+\frac{1}{10}=\left(\frac{1+3}{30}\right)$
$\Rightarrow \frac{1}{R}=\frac{4}{30}$
$\Rightarrow R=\frac{30}{4}=7.5\Omega$
Now, $9\Omega \&7.5\Omega$ are in series & we know,
for series,
$R_{eq}=R_1+R_2+R_3+...+R_n$
$\therefore R_{eq}=9+7.5=16.5\Omega$