Resistors in Parallel Formula:
In fig (2) the resistors are connected in parallel. There three resistors R1, R2 are connected in parallel between two points. Let I1, I2, & I3 current passing through resistors R1, R2 and R3 respectively. V is potential differences between two ends.
The total current flowing through the circuit is the sum of currents flowing through each resistor.
I = I, + I2 + I3 —– (1)
Rp is equivalent resistance in parallel combination.
According to Ohm’s law, I = V/Rp
Similarly,
I1 = V/R1, I2 = V/R2, I3 = V/R3
Substituting these value of current in equation (1)
V/Rp = V/R1 + V/R2, V/R3
∴ 1/Rp = 1/R1 + 1/R2 + 1/R3 —— (2)
The reciprocal of the equivalent resistance is equal to the sum of the reciprocal at individual resistances.
The resistors in parallel is used to reduce the resistance in a circuit. If ‘n’ no of resistors are connected in parallel then, equation (2) becomes 1/Rp = 1/R1 + 1/R2 + 1/R3 —– + 1/Rn —- (3)
Numericals on Resistors in Parallel Formula :
(1) Resistors having resistances of 25Ω, 30Ω and 20Ω are connected in parallel. What is the effective resistance in the circuit?
Given:
R1 = 25Ω, R2 = 30Ω and R3 = 20Ω
1/Rp = 1/R1 + 1/R2 + 1/R3
1/Rp = 1/25 + 1/30 + 1/20 (Take LCM 12+10+15/300)
1/Rp= 37/300
Rp = 300/37 = 8.1Ω
∴ Effective resistance in a circuit is 8.1Ω.
(2) Three resistor having resistances of 3Ω, 5Ω and 7Ω are connected in parallel and potential difference of 18 V is applied across them. Calculate the current flowing through individual resistors?
Given:
R1 = 3Ω, R2 = 5Ω, R3 = 7Ω
V = 18V
V = I
I = V/R
I1 = V/R1 = 18/3 = 6A
I2 = V/R2 = 18/5 = 3.6A
I3 = V/R3 = 18/7 = 2.57A
I = I1 + I2 + I3
= 6 + 3.6 + 2.57
I = 12.17 A
Total current flowing through the circuit is 12.17 A and current flowing through each resistor is 12.17 A.