How do you calculate the total resistance of a parallel circuit?

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How do you calculate the total resistance of a parallel circuit?

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Answer 1 · 2014-04-14T15:30:37

Use the resistance formula:

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Example:

You have 4 resistors all connected in parallel. R1 and R2 each have a resistance of 4 ohms, R3 and R4 each have a resistance of 8 ohms. What is the total resistance?

$\frac{1}{Rp}$ $1/"Rp"$ = $\frac{1}{R1}$ $1/"R1"$ + $\frac{1}{R2}$ $1/"R2"$ + $\frac{1}{R3}$ $1/"R3"$ + $\frac{1}{R4}$ $1/"R4"$

$\frac{1}{Rp}$ $1/"Rp"$ = $\frac{1}{4}$ $1/4$ + $\frac{1}{4}$ $1/4$ + $\frac{1}{8}$ $1/8$ + $\frac{1}{8}$ $1/8$

(Find a common denominator)

$\frac{1}{Rp}$ $1/"Rp"$ = $\frac{2}{8}$ $2/8$ + $\frac{2}{8}$ $2/8$ + $\frac{1}{8}$ $1/8$ + $\frac{1}{8}$ $1/8$

$\frac{1}{Rp}$ $1/"Rp"$ = $\frac{6}{8}$ $6/8$

(Rp is the reciprocal of this)

Rp = $\frac{8}{6}$ $8/6$ = 1.33 ohms

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How do you calculate the total resistance of a parallel circuit?

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