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Find the equivalent resistance between two points A and B in the adjacent circuit

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16 Ω

14 Ω

11 Ω

18 Ω

answer is B.

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Detailed Solution

The equivalent resistance between two points

A and B

in the adjacent circuit is given by

14 Ω

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} + \frac{1}{R_{}} + \frac{1}{R_{}}

\Rightarrow \frac{1}{R_{AB}} = \frac{1}{3} + \frac{1}{3_{}} + \frac{1}{3_{}} + \frac{1}{6} + \frac{1}{6_{}} + \frac{1}{4_{}} + \frac{1}{4_{}}

= \frac{4 + 4 + 4 + 2 + 2 + 3 + 3}{12_{}}

\Rightarrow \frac{1}{R_{AB}} = \frac{22}{12}

\Rightarrow 22 \times R_{AB} = 12

\Rightarrow R_{AB} = \frac{12}{22}

= 0.545

\Rightarrow R = 1 + 4 + 4 + 4 + 0.545

= 13.545

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