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Resistors in parallel

The equivalen...

Question

The equivalent resistance R of three resistors $R_{1}$ , $R_{2}$ and $R_{3}$ joined in parallel is

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

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R = 1 / R_{1} + 1 / R_{2} + 1 / R_{3}

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

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R = 1 / (R_{1} + R_{2} + R_{3})

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Solution

The correct option is C $R = \frac{R_{1} R_{2} R_{3}}{R_{1} R_{2} + R_{2} R_{3} + R_{3} R_{1}}$
Equivalent resistance $R$ is given by:
$\frac{1}{R} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}}$
$\Rightarrow R = \frac{R_{1} R_{2} R_{3}}{R_{1} R_{2} + R_{2} R_{3} + R_{3} R_{1}}$

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Similar questions

- 1

Δ A B C

a < b < c

r

r_{1}, r_{2}, r_{3}

A, B, C

r < r_{1} < r_{2} < r_{3}

- 2

Δ A B C

r_{1} r_{2} + r_{2} r_{3} + r_{3} r_{1} = \frac{r_{1} r_{2} r_{3}}{r}

△ A B C

a < b < c

r

r_{1}, r_{2}, r_{3}

A, B, C

r < r_{1} < r_{2} < r_{3}

△ A B C, r_{1} r_{2} + r_{2} r_{3} + r_{3} r_{1} = \frac{r_{1} r_{2} r_{3}}{r}

Δ

r_{1} + r_{2} + r_{3} - r = 4 R

r_{1} r_{2} + r_{2} r_{3} + r_{3} r_{1} = Δ^{2}

r_{1}, r_{2}, r_{3}

\frac{1}{r_{1}} + \frac{1}{r_{2}} + \frac{1}{r_{3}} - \frac{1}{r}

r_{1}, r_{2}, r_{3}

\frac{1}{r_{1}} + \frac{1}{r_{2}} + \frac{1}{r_{3}} - \frac{1}{r}

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