Question

Calculate equivalent resistance between $AandB$ from the following diagram:

Answer 1

Step-1 Given data and circuit diagram

Resistance $3\Omega and2\Omega$ are in series and resistance $6\Omega and4\Omega$ are also in series and they are in parallel combination with $30\Omega$.

Step-2 Finding equivalent resistance in the series combination

Equivalent resistance in series combination is given by the formula $R_{eq}=R_1+R_2+R_3+....$

Resistance $3\Omega and2\Omega$ are connected in a series combination. So, the equivalent resistance of $3\Omega and2\Omega$ is

$R\text{'}=3+2$

$R\text{'}=5\Omega$

Resistance $6\Omega and4\Omega$ are also connected in series combination. So, the equivalent resistance of $6\Omega and4\Omega$ is

and $R\text{'}\text{'}=6+4$

$R\text{'}\text{'}=10\Omega$

Now redraw the circuit diagram.

Step-3 Finding equivalent resistance in parallel combination.

Equivalent resistance in parallel combination is given by the formula $\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}$

Resistance $R\text{'}=5\Omega$, $R\text{'}\text{'}=10\Omega$and $30\Omega$are connected in parallel combination. So, the equivalent resistance$\left(R_{eq}\right)$ between $AandB$ can be evaluated using the above formula.

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

$\frac{1}{R_{eq}}=\frac{6+3+1}{30}$

$\frac{1}{R_{eq}}=\frac{10}{30}$

$R_{eq}=3\Omega$

Hence, the equivalent resistance between $AandB$ of the given circuit $3\Omega$.