Explanation – Conductance is the opposite of resistance, the measure of how easy is it for electrons to flow through something. The formula we use is:

Conductance = 1/Resistance.

The greater the resistance, the less the conductance, and the less the resistance, the greater the conductance. We use this when doing a parallel circuit equation. Total parallel resistance is less than the separate branch’s resistances because parallel resistors resist less together than they do separately. This means that Total parallel conductance is great than the separate branch’s conductances because parallel resistors conduct more together than they do separately. This can be seen in the formula:

G=conductance

G (total) = G (1) + G (2) + G (3) + . . .

So since the resistance is the reciprocal of conductance, then,

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1/R (total) = 1/R (1) + 1/R (2) + 1/R (3) + . . .

This is why we use the formula -

1/R (total) = 1/R (1) + 1/R (2) + 1/R (3) + . . .

when finding the resistance in parallel circuits.

Applications:

These ideas benefit us every day.

We use the formula
1/R (total) = 1/R (1) + 1/R (2) + 1/R (3) + . . . when solving for
resistance in parallel circuits, and this explains why we would divide
resistance by one, rather than just adding the resistances.

Question – What is the total resistance of a parallel circuit with 3
resistors with resistances of 3 ohms, 4 ohms, and 5 ohms.

Answer – 1/R (total) = 1/R (1) + 1/R (2) + 1/R (3)

1/R (total) = (1/3) + (1/4) + (1/5)

R (total) = 1.28 ohms

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Gregory Shepertycky