Question

In the arrangement of resistances shown below, the effective resistance between points A and B is

• A. $20\Omega$
• B. $30\Omega$
• C. $90\Omega$
• D. $110\Omega$

Answer 1

The correct option is A

$20\Omega$

Step 1: Given data

Step 2: Formula used

For resistors connected in parallel,

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

For resistors connected in series,

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

Step 3: Finding the effective resistance

From the figure, we can see that all the pairs of resistances in the upper and lower branch are in $1:2$ ratio, which indicated that the circuit obeys Wheatstone's bridge principle. So there is no current flowing through the vertical branches. The circuit becomes as shown.

Here, the effective resistance,

$$\begin{gathered} \frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2} \\ Here{R}_1=30ohmand{R}_2=60ohm \\ \Rightarrow \frac{1}{R_{eq}}=\frac{1}{30}+\frac{1}{60} \\ \Rightarrow \frac{1}{R_{eq}}=\frac{3}{60} \\ \Rightarrow R_{eq}=20\Omega \end{gathered}$$

The effective resistance between points A and B is $20\Omega$

Option A is correct