5 |  parallel circuit

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.

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)

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)