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What is the Resistance of a Parallel Circuit?

The total
resistance (R total)
of a

parallel
circuit is calculated using the formula

^{1}/_{R}_{ }_{total}
= ^{1}/_{R1} + ^{1}/_{R2} + ^{1}/_{R3} ·····

In the above circuit,

^{1}/_{R}_{ }_{total}
= ^{1}/_{2} + ^{1}/_{3} + ^{1}/_{4}

= ^{6}/_{12} +
^{4}/_{12}
+ ^{3}/_{12}

^{1}/_{R}_{ }_{total}
= ^{13}/_{12
}

R total
= ^{12}/_{13
}

= 0·92 ohms.

Notice that this is a much smaller resistance

than a series circuit using
the same
resistors.

It is even
smaller than the smallest
resistor

in the parallel circuit above, which is 2
ohms.

Adding a resistor
in an extra branch
decreases

the total
resistance of
a parallel circuit

because the electricity
has more paths to flow
along

and so the total current
flowing increases.

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