Question

Find the equivalent resistance between A & B in the circuit given below.

• A. $49\Omega$
• B. $16.5\Omega$
• C. $8.5\Omega$
• D. $18\Omega$

Answer 1

The correct option is B $16.5\Omega$

Equivalent resistance for series connection is:
$R_{eq}=R_1+R_2+R_3+...+R_n$
Since $12\Omega \&18\Omega$ are in series, we can can calculate the equivalent resistance for this combination, $R_{1eq}=12+18=30\Omega$

For parallel connection, equivalent resistance,
$\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...+\frac{1}{R_n}$
Now, $R_{1eq}\&10\Omega$ are in parallel
Therefore, equivalent resistance for this combination is:
$\therefore \frac{1}{R_{2eq}}=\frac{1}{R_{1eq}}+\frac{1}{10}=\frac{1}{30}+\frac{1}{10}=\left(\frac{1+3}{30}\right)$
$\Rightarrow \frac{1}{R_{2eq}}=\frac{4}{30}$
$\Rightarrow R_{2eq}=\frac{30}{4}=7.5\Omega$
Now, $9\Omega \&R_{2eq}$ are in series.
$\therefore$ Equivalent resistance for this combination is:
$R_{3eq}=9+R_{2eq}=9+7.5=16.5\Omega$.