Problem 7: Resistors of 20Ω, 40Ω and 50Ω, are connected in parallel across a 50V power source. Find the equivalent resistance of the set and the current in each resistor.
Since I=V/R,
V/R = V/R1+V/R2+V/R3+...+V/Rn
V(1/R)=V(1/R1+1/R2+1/R3+...+1/Rn)
1/R=1/R1+1/R2+1/R3+...+1/Rn
Above equation is used to find equivalent resistance of resistors connected in parallel.
Solution:
Step: 1 Overview
Parallel combination of resistors.
In this combination each resistor is connected to one common point, and hence each resistor will get same amount of voltage, but current will be divided according to amount of resistance in each resistor. Hence,
I = I1+I2+I3+...+InSince I=V/R,
V/R = V/R1+V/R2+V/R3+...+V/Rn
V(1/R)=V(1/R1+1/R2+1/R3+...+1/Rn)
1/R=1/R1+1/R2+1/R3+...+1/Rn
Above equation is used to find equivalent resistance of resistors connected in parallel.
Step: 2 Calculation
Given:R1=20ΩRequired:
R2=40Ω
R3=50Ω
V=50V
Equivalent Resistance of circuit (R)=?Solution:
I1=?
I2=?
I3=?
From above equation:
1/R=1/R1+1/R2+1/R3
1/R=(1/20)+(1/40)+(1/50)
1/R=(10+5+4)/200
1/R=19/200
R=200/19
R=10.53Ω
I1=V/R1
I1=50V/20Ω
I1=2.5AI2=V/R2
I2=50V/40Ω
I2=1.25AI3=V/R3
I3=50V/50Ω
I3=1A
R=10.53Ω, I1=2.5A, I2=1.25A and I3=1A (Ans)
