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SS1: PHYSICS – 3RD TERM

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Resistance in Parallel

When resistors are placed in parallel, they are arranged side by side with their ends joined together. With the arrangement, the potential difference across the resistors is the same.

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The equipment parallel resistance Rtotal is found using the expression,

I = I1 + I2 + I3 ____________________ (1)

Since the current flowing through each resistor is 

I1 = \( \frac{V}{R_1}\) I2 = \( \frac{V}{R_2}\) I3 = \( \frac{V}{R_3}\)   __________________ (2)

Substituting these equation (1) in *

 ∴ I = \( \frac{V}{R_1} + \frac{V}{R_2} + \frac{V}{R_3} =\frac{V}{R_{Total}}\)

= \( \scriptsize V \left ( \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} \right)\)

∴  \(\frac{1}{R_Total} = \frac{1}{R_1}+ \frac{1}{R_2} + \frac{1}{R_3}\)

For two resistors in parallel

Screen Shot 2020 10 20 at 12.51.26 AM

Total Resistance = \( \frac {R_1 R_2}{R_1 + R_2} \)

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