Question

Prove 1/req=1/R1+1/R2+1/R3 in parallel connection of resistance.

Answer 1

Hope it helps........

Answer 2

Concept:

• Electric circuits
• The parallel arrangement of resistors

Given:

• Equivalent resistance = Req
• Given resistances: R1, R2, R3
• Resistors are in a parallel arrangement
• Potential difference = V
• Current flowing through main circuit = I
• Current flowing through R1 = I1
• Current flowing through R2 = I2
• Current flowing through R3 = I3

Find:

• The formula for equivalent resistance for resistors in a parallel arrangement

Solution:

The current in the main circuit has to be equal to the sum of the currents in the individual branches flowing through the resistors

I = I1 + I2 + I3

We know that V = IR, I = V/R.

We also know that the potential difference across each resistor is equal.

I1 = V/R1

I2 = V/R2

I3 = V/R3

V/Req = V/R1 + V/R2 + V/R3

1/Req = 1/R1 + 1/R2 + 1/R3

Therefore, 1/Req = 1/R1 + 1/R2 + 1/R3

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