Question

Calculate the equivalent resistance between A and B from the following diagram:

Answer 1

Hint : Here, we can say that the resistors are in three pairs and these pairs are parallel to each other. Therefore, we will use the formula of equivalent resistance in case of series combination. Also, we will use the formula of equivalent resistance in case of parallel combination to calculate the equivalent resistance between A and B.
The formula of equivalent resistance in series combination is given below
${R_{eq}} = {R_1} + {R_2} + {R_3} + .......$
Here, ${R_{eq}}$ is the equivalent resistance of the resistors in series combination and ${R_1}$ , ${R_2}$ , ${R_3}$ ……. are the resistors in series.
Also, the formula of equivalent resistance in parallel combination is given below
$\dfrac{1}{{{R_{eq}}}} = \dfrac{1}{{{R_1}}} + \dfrac{1}{{{R_2}}} + \dfrac{1}{{{R_3}}} + ......$
${R_{eq}}$ is the equivalent resistance of the resistors in parallel combination and ${R_1}$ , ${R_2}$ , ${R_3}$ ……. are the resistors in parallel combination.

Complete Step By Step Answer:
At first we will calculate the resistance in series of each pair one by one as given below
${R_1} = 3\Omega + 2\Omega = 5\Omega$
${R_2} = 30\Omega$
${R_3} = 6\Omega + 4\Omega = 10\Omega$
Therefore, the circuit given in the question will become

Now, we will use the formula of equivalent resistance in case of parallel resistors to calculate the resistance of the three resistors.
Therefore, the equivalent resistance between A and B is calculated below
$$ \dfrac{1}{{{R_{eq}}}} = \dfrac{1}{{{R_1}}} + \dfrac{1}{{{R_2}}} + \dfrac{1}{{{R_3}}} $$
$\Rightarrow \,\dfrac{1}{{{R_{eq}}}} = \dfrac{1}{5} + \dfrac{1}{{30}} + \dfrac{1}{{10}}$
$\Rightarrow \,\dfrac{1}{{{R_{eq}}}} = \dfrac{{6 + 1 + 3}}{{30}}$
$\Rightarrow \,\dfrac{1}{{{R_{eq}}}} = \dfrac{{10}}{{30}}$
$\Rightarrow \,\dfrac{1}{{{R_{eq}}}} = \dfrac{1}{3}$
$\Rightarrow \,{R_{eq}} = 3\Omega$
Therefore the equivalent resistance between A and B is $3\,\Omega$ .

Note :
For the resistances which will be series, the voltage and the current flowing through the circuit will be the same. On the other hand, for the resistance will be in parallel combination, the voltage will be the same but the current flowing through the circuit will depend on the value of resistance.