Combination CircuitsCombination Circuits

Steps to Solve Combined Series-Parallel CircuitsSteps to Solve Combined Series-Parallel Circuits

1. If necessary, draw a diagram of the circuit.2. Find any parallel resistors in the circuit and simplify

them into one equivalent resistance using the formula for parallel equivalent resistance.

3. If necessary, draw a new diagram using the equivalent resistor instead of the multiple previous resistors.

4. Find any resistors that are now in series and replace them with the equivalent resistance using the formula for series equivalent resistance.

5. If necessary, draw a new diagram using the equivalent resistance.

6. Once the circuit is reduced into a single resistor, you can now solve for the current using Ohm’s Law.

Calculate the following:

a)total equivalent resistance

b)total current

c)the current across each resistor

d)the voltage drop across each resistor

Draw the Circuit

Solve for Req for parallel resistors

1/Req = 1/4 + 1/12

1/Req = .333

Req = 3 ΩRemember, the first step in combination

circuits is ALWAYS to calculate the

equivalent resistance of the parallel

resistors!

Redraw the Circuit

5 Ω

3 Ω

8 Ω

24 V

Solve for Req for series resistors

Req = 8 + 3 + 5

Req = 16 ΩNote: the 3Ω

resistor came from the result of our

solving for the Req for the parallel circuit section

5 Ω

3 Ω

8 Ω

24 V

Redraw the Circuit

24 V

16 Ω

Solve for the Total Current

Vt = (It)(Rt)

24 = It(16)

It = 1.5 amps

Ohm’s Law:V = IR

Since resistors R1 and R4 are in series, the current in series-connected resistors is the same everywhere. Therefore,

It = I1 = I4 = 1.5 amps

Solve for the Current through Each Resistor

Note: In a Series Circuit, to solve for total current: It = I1 = I2 = I3 =…

Since resistors R2 and R3 are in parallel, the current in parallel-connected resistors is added up to equal the total current. Therefore,

It = I1 + I4 = 1.5 amps

Solving for the Current through Each Resistor

However, this gets a bit tricky because the resistors do not have the same value; therefore we must first calculate the voltage drop through each resistor and then come back to calculate the current

Calculate the voltage drop across the series-connected resistors. (R1 and R4 in diagram)

V1 = I1R1 V4 = I4R4

V1 = (1.5)(5) = 7.5 V V4 = (1.5)(8) = 12 V

Series Circuit, to solve for total voltage: Vt = V1 + V2 + V3 +…

Next, subtract the values for the series voltage from the total voltage

VT – Vseries = Vparallel 24 V – 7.5 V – 12 V = 4.5 V

This tells us that the voltage drop across EACH parallel resistor is 4.5 V because

Vt = V1 = V2 = V3 = …

Lastly, using Ohm’s Law calculate the current traveling through each parallel resistor

V2 = I2R2 V3 = I3R3 4.5 = I2(4) 4.5 = I3(12) I2 = 1.125 amps I3 = .375 amps

Remember, current varies through each

parallel resistor since there is more than one path for the

electrons to take!

Results of our calculations: