Electrical Engineering Principles
Next topic >> AC Principles
What is parallel circuit ?
A parallel circuit has two or more paths for current to flow through. Voltage is the same across each component of the parallel circuit. The sum of the currents through each path is equal to the total current that flows from the source. The circuit is all load or resistors connected in same line with supply.
Two resistor in parallel
Two resistor connected in this configuration same together with the supply point.
Figure 1 parallel circuit with 2 resistors or loads connected.
Parallel Rules and Formula - 2 resistors in parallel
Total resistance is the proportion of total value,
Formula 1 Rt = (R1 x R2) ÷ (R1 + R2)
Formula 2 1/Rt = (1/R1) + (1/R2)
Total voltage remains the same across all point,
Vt = VR1 = VR2
Total current can apply this formula
Formula 1 Current total, It = Vt ÷ Rt or It = IR1 + IR2
Formula 2 Individual current at resistor 1, IR1 = Vt ÷ R1
Formula 3 Individual current at resistor 2, IR2 = Vt ÷ R2
Example calculation
1) Resistor 1 is 50Ω and Resistor 2 is 80Ω , find total resistance, Rt?
Solution: Rt = (R1 x R2) ÷ (R1 + R2)
Rt = (50Ω x 80Ω) ÷ (50Ω + 80Ω) = 30.76 Ω
2) (a) Resistor 1 is 120Ω and Resistor 2 is 350Ω , find total resistance, Rt?
Solution: Rt = (R1 x R2) ÷ (R1 + R2)
= (120Ω x 350Ω) ÷ (120Ω + 350Ω) = 89.36 Ω
(b) Total voltage in the circuit is 100 vDC, calculate current across R1 and R2?
Solution: Current at resistor 1; IR1 = Vt ÷ R1 = 100v ÷ 120Ω = 0.83 A
Current at resistor 2; IR2 = Vt ÷ R2 = 100v ÷ 350Ω = 0.28 A
Total current ; (It) = IR1 + IR2 = 0.83A + 0.285A = 1.11 A
Verify using ; It = Vt ÷ Rt = 100v ÷ 89.36 Ω = 1.11 A (true)
Three or more resistors
When three (3) or more loads are connected in parallel the rules and behavior apply same.
Figure 2 three(3) resistors in parallel
Rules and Formula for 3 or more resistors
Total resistance is the proportion of total value,
Formula 1 Rt = 1 ÷ ((1÷R1)+(1÷R2)+(1÷R3))
Formula 2 1/Rt = (1÷R1) + (1÷R2) + (1÷R3)
Total voltage remains the same across all point,
Voltage total, Vt = VR1 = VR2 = VR3
Total current can apply this formula
Formula 1 It = IR1 + IR2 + IR3 or It = Vt ÷ Rt
Formula 2 Individual current at resistor 1, IR1 = Vt ÷ R1
Formula 3 Individual current at resistor 2, IR2 = Vt ÷ R2
Formula 4 Individual current at resistor 3, IR3 = Vt ÷ R3
Example calculation
1) Given R1 = 20Ω, R2 = 40Ω and Resistor 3 is 80Ω , find total resistance, Rt?
Solution: Rt = 1÷((1÷R1)+(1÷R2)+(1÷R3))
Rt = 1÷((1÷20Ω)+(1÷40Ω)+(1÷80Ω)) = 11.42 Ω
2) (a) R1 is 10Ω, R1 is 20Ω and R3 is 35Ω , find total resistance, Rt?
Solution: Rt = 1÷((1÷R1)+(1÷R2)+(1÷R3))
Rt = 1÷((1÷10Ω)+(1÷20Ω)+(1÷35Ω)) = 5.6 Ω
(b) Total voltage in the circuit is 150 volt DC, calculate current across R1, R2 and R3?
Solution: Current at resistor 1; IR1 = Vt ÷ R1 = 150v ÷ 10Ω = 15 A
Current at resistor 2; IR2 = Vt ÷ R2 = 150v ÷ 20Ω = 7.5 A
Current at resistor 3; IR3 = Vt ÷ R3 = 150v ÷ 35Ω = 4.28 A
Total current ; It = IR1 + IR2 + IR3 = 15A + 7.5A + 4.28A = 26.78 A
Verify using ; It = Vt ÷ Rt = 150v ÷ 5.6 Ω = 26.78 A (true)