Three resistors are connected in the order of the sides of a triangle ABC as shown in the figure. The equivalent resistance between the end of A and B will be.

Correct option is C

Step 1: Circuit Analysis

The circuit is a triangle (Delta) configuration, where:

• Resistance between $A$ and $C$: $60\Omega$
• Resistance between $C$ and $B$: $100\Omega$
• Resistance between $A$ and $B$: $40\Omega$

We are tasked with finding the equivalent resistance between $A$ and $B$.

Step 2: Combine Resistors Between Paths

Resistors $100\Omega$ (between $C$ and $B$) and $60\Omega$ (between $A$ and $C$) are in series:

R_series=100+60=160Ω 

Step 3: Parallel Combination of $R$ and $40\Omega$ (directly between $A$ and $B$):

The equivalent resistance of two resistors in parallel is given by:

R_parallel    = 

    

Here, R1=160ΩR_1 = 160 \, \OmegaR1​=160Ω and R2=40ΩR_2 = 40 \, \OmegaR2​=40Ω. Substituting the values:

 

​

The equivalent resistance between $A$ and $B$ is:

RAB=32ΩR_{AB} = 32 \, \OmegaRAB​=     32Ω       

The equivalent resistance between AAA and BBB is 32 Ω.