SKILL 2
SOLVE A COMBINATION CIRCUIT
Procedure Overview
In this procedure, you will solve combination circuits using the seven-step
process. You will calculate voltage and current values for each resistance in the
circuit and redraw the circuit with all the values listed. In step 1, you will be
led through the process. In steps 2 and 3, you will do it yourself.

1. Perform the following substeps to simplify the combination circuit shown in
figure 2-1.

The total resistance in a combination circuit can be found by combining the
equations used to find total resistance in a series circuit and a parallel circuit.
For example, the total resistance of the combination circuit in figure 2-1 is
found by first calculating the equivalent resistance of the two resistors that
are in parallel, R2 and R3. This resistance is then added to the resistances that
are in series with it, R1 and R4.

The following substeps will lead you through this process.
R1= 25
(R2 R3= REQ)
+
24V
R2=
50
R3=
10
R4= 25
Figure 2-1.
Calculating Total Resistance
LB227-BC05UEN-E1-S02, REV. C COMBINATION CIRCUITS
Copyright © 2019 Amatrol, Inc.
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SKILL 2 SOLVE A COMBINATION CIRCUIT
A. Calculate the equivalent resistance of R2 and R3 in the circuit in figure 2-1.
REQ = _____________________________________________ (Ohms)
REQ = _____________________________________________ (Ohms)
This is found as follows:
1
REQ
1
REQ
=
=
1
R2
1
50
+
+
1
R3
1
10
REQ = 8.33 ohms
The equivalent resistance is 8.33 ohms.
B. Calculate the total resistance of the circuit.
Since this equivalent resistance is in series with R1 and R4, you can now
find the total resistance by applying the formula for calculating total
resistance in a series circuit.
RT = _______________________________________________ (Ohms)
The answer is found as follows:
RT = R1 + REQ + R4 (Where REQ is the equivalent resistance
of R2 and R3 in parallel.)
RT = R1 + REQ + R4
RT = 25 + 8.33 + 25
RT = 58.33
The circuit in figure 2-1 has the same resistance as a circuit with just one
load with the resistance of 58.33 ohms.
This completes steps 1 and 2 of the seven step process.
C. Calculate the total current in the circuit of figure 2-1.
Since the source voltage and the total resistance are known, they can be
used to calculate the total current (IT) using Ohms Law.
IT = _______________________________________________ (Amps)
The answer is found as follows:
IT =
VT
RT
IT =
24
58.33
IT = .41
Total current in the circuit is approximately 0.41 amps.
LB227-BC05UEN-E1-S02, REV. C COMBINATION CIRCUITS
Copyright © 2019 Amatrol, Inc.
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SKILL 2 SOLVE A COMBINATION CIRCUIT
D. Calculate the voltage drops across the resistors in the circuit in figure 2-1.
In figure 2-2, the circuit from figure 2-1 has been reduced to a series circuit
using the equivalent resistance calculated for the two parallel resistors.
Since the current is known, the voltage drop across each resistance can
now be calculated using Ohms Law.
R1 = 25
+
REQ = 8.33
24V
R4 = 25
Figure 2-2.
Combination Circuit to a Series Circuit
VR1 = _______________________________________________ (VDC)
VREQ = ______________________________________________ (VDC)
VR4 = _______________________________________________ (VDC)
The answers are found as follows:
VR1 = IT × R1
VR1 = 0.41 × 25
VR1 = 10.25 volts
VREQ = IT × REQ
VREQ = 0.41 × 8.33
VREQ = 3.42 volts
VR4 = IT × R4
VR4 = 0.41 × 25
VR4 = 10.25
The voltage drop across R1 is 10.25 volts. The voltage drop across REQ is
3.42 volts. The voltage drop across R4 is also 10.25 volts.
NOTE
The total calculated voltage is not quite 24V because we rounded off our
calculations.
LB227-BC05UEN-E1-S02, REV. C COMBINATION CIRCUITS
Copyright © 2019 Amatrol, Inc.
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SKILL 2 SOLVE A COMBINATION CIRCUIT
Since the voltage across the equivalent resistance of R2 || R3 is 3.42 volts,
we can say that the voltage drop across each of the parallel resistors, R2
and R3 is 3.42 volts, as shown in figure 2-3.
VR1= 10.25V
+
24V
R2
R3
VR2/3 = 3.42V
VR4 = 10.25V
Figure 2-3.
Voltage Drops in a Combination Circuit
E. Calculate the current in each branch of the circuit in figure 2-1.
Figure 2-4 shows the updated circuit.
VR1 = 10.25V
R1=25
IT
+
I R2
24V
R2=50
IR3
R3=10
VREQ=3.42V
IT
R4=25
VR4=10.25V
Figure 2-4.
Current Flow in a Combination Circuit
LB227-BC05UEN-E1-S02, REV. C COMBINATION CIRCUITS
Copyright © 2019 Amatrol, Inc.
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SKILL 2 SOLVE A COMBINATION CIRCUIT
The current in each branch of the parallel section can now be calculated
by dividing the voltage drop of each load by its resistance.
IR2 = _______________________________________________ (Amps)
IR3 = _______________________________________________ (Amps)
The answers are found as follows:
IR2 =
VR 2
R2
IR2 =
3.42
50
I R 2 = .068 A
I R3 =
VR3
R3
I R3 =
3.42
10
I R3 = .342 A
The current in branch R2 (IR2) is 0.068 A or 68 mA. The current in branch
R3 (IR3) is 0.342 A or 342 mA.
The branch currents are shown in figure 2-5.
R1
+
24V
R2
I R2 =
68mA
I R3 =
342mA
R3
R4
Figure 2-5.
Branch Currents in a Combination Circuit
If the branch currents are added, the sum should equal the total current
that flows through the circuit. This is according to Kirchhoffs Current
Law.
LB227-BC05UEN-E1-S02, REV. C COMBINATION CIRCUITS
Copyright © 2019 Amatrol, Inc.
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SKILL 2 SOLVE A COMBINATION CIRCUIT
F. Draw the circuit from figure 2-4 with all values shown.
Your circuit should look like figure 2-6.
R1= 25
VR1 = 10.25V
IT = 0.41mA
+
24V
VR3 = 3.42V
VR2 = 3.42V R3=10
R2 = 50
I R3 = 342mA
I R2 = 68mA
R4= 25
VR4 = 10.25V
Figure 2-6.

Circuit Solved
2. Perform the following substeps to solve the circuit in figure 2-7.
R1 = 25
R3 =
50
+
R2 =
50
120V
R5 = 100
R4 =
25
R6 = 25
Figure 2-7.
Combination Circuit
A. Calculate the equivalent resistance of R2 || R3 (REQ1) and R5 || R6 (REQ2) for
the circuit in figure 2-7.
REQ1 = _____________________________________________ (Ohms)
REQ2 = _____________________________________________ (Ohms)
They should be REQ1 = 25 ohms and REQ2 = 20 ohms.
LB227-BC05UEN-E1-S02, REV. C COMBINATION CIRCUITS
Copyright © 2019 Amatrol, Inc.
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SKILL 2 SOLVE A COMBINATION CIRCUIT
B. Calculate the total resistance (RT) of the circuit.
RT = _______________________________________________ (Ohms)
RT should = 95 ohms.
C. Calculate the total current (IT) using the source voltage and RT.
IT = _______________________________________________ (Amps)
IT should = 1.263A.
D. Calculate the voltage drops across the series resistances, including the
equivalent resistances.
VR1 = _______________________________________________ (Volts)
VREQ1 = _____________________________________________ (Volts)
VR4 = _______________________________________________ (Volts)
VREQ2 = _____________________________________________ (Volts)
They should be VR1 = 31.58V, VREQ1 = 31.58V, VR4 = 31.58V, and
VREQ2 = 25.26V.
E. Determine the current in the branches of the parallel sections.
IR2 = _______________________________________________ (Amps)
IR3 = _______________________________________________ (Amps)
IR5 = _______________________________________________ (Amps)
IR6 = _______________________________________________ (Amps)
They should be IR2 and IR3 = .632A, IR5 = .253A, and IR6 = 1.01A.
F. Calculate the voltage of each parallel resistance using the current and
resistance values.
VR2 = _______________________________________________ (Volts)
VR3 = _______________________________________________ (Volts)
VR5 = _______________________________________________ (Volts)
VR6 = _______________________________________________ (Volts)
They should be VR2 and VR3 = 31.58V, and VR5 and VR6 = 25.26V. VR2 and
VR3 should be the same because they are in parallel, as should VR5 and VR6.
G. Redraw the circuit and list the voltage and current for each resistor along
with its resistance.
LB227-BC05UEN-E1-S02, REV. C COMBINATION CIRCUITS
Copyright © 2019 Amatrol, Inc.
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SKILL 2 SOLVE A COMBINATION CIRCUIT

3. Now solve the circuit in figure 2-8. Show all your work.
R1 = 10
R2 = 10
+
12V
R3 =
25
R6 = 10
Figure 2-8.
R4 =
100
R5 = 50
Combination Circuit
LB227-BC05UEN-E1-S02, REV. C COMBINATION CIRCUITS
Copyright © 2019 Amatrol, Inc.
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