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If three resistors of resistances $2 Ω$ , $3 Ω$ and $6 Ω$ are connected in parallel, then what is the equivalent resistance?

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1 Ω

5 Ω

9 Ω

None of the above

answer is B.

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Detailed Solution

The equivalent resistance is

1 Ω

.
Given,
The first resistance,

R_{1} = 2 Ω

The second resistance,

R_{2} = 3 Ω

The third resistance,

R_{3} = 6 Ω

It is known that “When the resistances are connected in parallel, the reciprocal of the equivalent resistance is equal to the sum of the reciprocal of the individual resistances.” Mathematically,

\frac{1}{R} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} + . . . + \frac{1}{R_{n}}

Where

\frac{1}{R}

is the equivalent resistance and

\frac{1}{R_{1}}

\frac{1}{R_{2}}

\frac{1}{R_{3}}

, …,

\frac{1}{R_{n}}

are the individual resistances.
For three resistances, it can be written as

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

On substituting the given values, we get the equivalent resistance as

\Rightarrow \frac{1}{R} = \frac{1}{2} + \frac{1}{3} + \frac{1}{6}

\Rightarrow R = 1 Ω

Hence, the equivalent resistance is

1 Ω

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