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Lesson 2, Topic 3
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# Resistance in Parallel

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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.

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

Total Resistance = $$\frac {R_1 R_2}{R_1 + R_2}$$

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