The effective resistance between A and B, if the resistance of each resistor is R, will be:

Question

Accepted Answer

Given: The resistance of each resistor is $R$ .

Find: The effective resistance between A and B.

To find the effective resistance between points A and B, where each resistor has a resistance $R$ , we analyze the given circuit diagram step-by-step:

Circuit between A and B with outer resistors and a symmetric diamond bridge containing multiple resistors of value R, including horizontal and vertical middle branches.

Identify the configuration: The circuit forms a bridge.
Analyze symmetry: From symmetry, two middle resistances can be removed.
The simplified circuit becomes:

Stepwise simplification of the resistor network showing the symmetric bridge reduced to three parallel branches of 2R, then to 2R by 3, then total 8R by 3 between A and B.

After symmetry-based reduction, the network between the two inner junctions consists of three branches, each of resistance

2R

in parallel.

Hence their equivalent resistance is

\frac{1}{R_{eq}} = \frac{1}{2R} + \frac{1}{2R} + \frac{1}{2R} = \frac{3}{2R}

so,

R_{eq} = \frac{2R}{3}

Now this equivalent resistance is in series with the left and right resistors, each of resistance $R$ . Therefore,

R_{AB} = R + \frac{2R}{3} + R

R_{AB} = \frac{8R}{3}

Therefore, the effective resistance between A and B is $\frac{8R}{3}$ . The correct option is B.

Answer

Step-by-step solution

Common mistakes

Practice more Combination of Resistors questions

Related questions