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Deduce the expression for the equivalent resistance of three resistors connected in parallel.

(OR) 

Derive : 1/R = 1/R1 + 1/R2 + 1/R3

(OR) 

Explain the expression for the equivalent resistance of three resistors which are connected in parallel. 

(OR) 

If all the first ends of resistors are connected to and second ends are connected to another point, then what type of connection is this? Derive the resultant resistance for this connection.

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In parallel connection of resistors, there is same potential difference at the ends of the resistors. 

Hence the voltage in the circuit is equal to V. 

Let Ip I2 and I3 be the currents flowing through R1 , R2 and R3 resistors respectively. 

Hence, we can write I = I1 + I2 +I3

According to the Ohm’s law,

According to the Ohm's Law

(here Req is the equivalent resistance)

∴ The equivalent resistance of a parallel combination is less than the resistance of each of the resistors.

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