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Three equal resistances, each of the same value R, are joined as shown in the figure. The equivalent resistance between A and B is

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R

2 R

\frac{R}{2}

\frac{R}{3}

answer is D.

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Detailed Solution

Three equal resistances, each of the same value

R

, are joined as shown in the figure. The equivalent resistance between

A and B

\frac{R}{3}

Three resistors each of resistance

R

If connected in parallel the combined resistance will be

\frac{R}{3}

If connected in series it will be

3 R

.
The given circuit corresponds to a parallel combination of three equal resistances of value R.
Hence the equivalent resistance between

A and B

is given by

\frac{1}{R_{AB}} = \frac{1}{R} + \frac{1}{R_{}} + \frac{1}{R_{}}

\frac{1}{R_{AB}}

\frac{3}{R_{}}

\frac{1}{R_{AB}} = \frac{3}{R_{}}

3 R_{AB} = R

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

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