What is Series-Parallel Circuit ?

Definition

Series-Parallel circuit are networks that contain both series and parallel circuit configuration.

In other words, if we attach the series circuit and parallel circuit together. Then the resultant network will be series-parallel networks. Most of the time you will find this type of network in analyzing the circuit.

Here is an example of series-parallel networks.

Series-Parallel Networks- Elucidate Techno

Three resistors R1, R2, R3 are connected together. R1 is connected in series with the source. And R2 and R3 are in parallel.

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How to measure the resistance of the series-parallel network?

• In this circuit, from the identification of series circuit, we can’t identify any branch that in series connection at first instance.

• But R2 and R3 have two common terminals. So, R2 and R3 in parallel. So, these two branches will be reduced to one as an equivalence of R2||R3 or Rt'.

Reduced Circuit- Elucidate Techno

• Now from the reduced version of this circuit clearly shows the series connection between R1 and Rt' which can fulfill completely the identification of series circuit.
• So, the total resistance will be Rt=Rt'+R1.

So in that way, we can first simplify any network and then measure its total resistance.

 
Mathematical problem

Here in this circuit,

Series-Parallel Math Problem-Elucidate Techno

Resistances, R1= 3Ω, R2=5Ω, R3=6Ω. And source voltage, V= 5V.

• What will be the total resistance?
• What will be the current I1, V1?
• What will be the voltage V1, V2,  I2, I3?

Solution

• What will be the total resistance?

Here, as R2 and R3 in parallel,So, Rt’=R2||R3 

          Now, As Rt' and R1 is in series, Total resistance, Rt = Rt'+R1 = (2.73+3) Ω = 5.73Ω

• What will be the current I1, V1?

As, R1 is in series with source therefore, Is= I1 =0.87AVoltage, V1= I1 x R1= (0.87 x 3) = 2.61V

• What will be the voltage V1, V2,  I2, I3?

The Source Voltage, V= 5VSo, Source current, Is = V/Rt = (5/ 5.73)A = 0.87A

The equivalent resistance was found, Rt' = 2.73 Ω

So, the equivalent voltage will be, Vt’= Is x Rt' = 2.375V

As, R2 and R3 in parallel so V2=V3=Vt'= 2.375V

Current, I2= V2/R2= (2.375/ 5) A = 0.475A

Current, I3 = V3/R3= (2.375/ 6) A = 0.396A

So, the final circuit will be,

Series-Parallel Final Circuit-Elucidate Techno

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