Question

Find the resistance between $A$ and $B$ in the circuit given below:

Answer 1

Step 1: Given data

From the figure, the value of resistors are $2\Omega ,2\Omega ,2\Omega$ and $6\Omega$

Step 2: Formula used

In a series combination of resistors,

$R_s=R_1+R_2+R_3+...+R_n$

In parallel combination of resistors,

$\frac{1}{R_p}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...+\frac{1}{R_n}$

Step 3: Finding the equivalent of the three $2\Omega$ resistors connected in series

In a series combination of resistors,

$R_s=R_1+R_2+R_3+...+R_n$

Here,

$$\begin{gathered} R\text{'}=2+2+2 \\ \Rightarrow R\text{'}=6\Omega \end{gathered}$$

Step 4: Finding the equivalent resistance between $A$ and $B$

In parallel combination of resistors,

$\frac{1}{R_p}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...+\frac{1}{R_n}$

Here,

$$\begin{gathered} \frac{1}{R}=\frac{1}{6}+\frac{1}{R\text{'}} \\ \Rightarrow \frac{1}{R}=\frac{1}{6}+\frac{1}{6} \\ \Rightarrow R=3\Omega \end{gathered}$$

Therefore, the resistance between $A$ and $B$ is $3\Omega$.