The document details concepts of electrical engineering, specifically focusing on the calculation of total resistance in series and parallel resistor configurations. It explains formulas for determining current and voltage drops across resistors, as well as applying Kirchhoff's current law. Examples and calculations illustrate the principles of combination circuits in a clear manner.

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Industrial Electronics N2
Resistors in Parallel
Resistors in Series
Combination of Resistors in Parallel
and Resistors in Series

4. 1.1The figure below shows two resistors in series.
Fig 1
Resistors in series are added up.
RT = (5 + 10) Ohms = 15 Ohms
The equivalent circuit based on the total
resistance of 15 Ohms becomes:
Fig 2
R1 = 5Ω R2 = 10Ω
12 V
RT = 15Ω
12 V
IT
IT

5. The total current IT flowing through the circuit is
given by the formula.
V = IT RT
Making IT the subject of the formula:
IT = V÷ RT
Thus, IT = 12 V ÷ 15Ω = 0.8 A
Voltage drop at Resistor 5 Ω = IT X R1
= 0.8A X 5 Ω = 4V
Voltage drop at Resistor 5 Ω = IT X R1
= 0.8A X 10 Ω = 8V
We can confirm our answer by adding:
V1 + V2 = VT or 4V + 8V = 12V

6. R1 = 5Ω R2 = 10Ω
12 V
IT
V1 V2
R1 = 5Ω
R2 = 10Ω
12 V
I1
I2
IT
Fig 2
Fig 3 The sum of voltage drops across resistors
Fig 4 Resistors in Parallel
A

7. 1.2 Resistors in Parallel
Fig 4 shows two resistors in parallel.
The voltage across R1 = Voltage across R2
V1 = V2 =VT
The total Resistance RT can be calculated thus:
1 = 1 + 1
RT R1 R2
1 = R2+ R1 making RT subject of the formula
RT R1R2
RT = R1R2 substituting RT = 5X 10 = 3.33Ω
R2+ R1 5 + 10

8. Similarly, IT = V/RT = 12V/3.33 Ω = 3.604 A
Applying Kirchhoff's Current law to node A
IT = I1 + I2
This means that I1 and I2 ,have been divided in a
certain ratio such that:
VT = I1 X R1 and VT = I2 X R2
Thus : I1 = VT and I2 = VT
R1 R2
Substituting these values into Equation IT = I1 + I2
IT = VT + VT = 12V + 12V = 2.4 A + 1.2 A = 3.6A
R1 R2 5 10

9. R3 = 10Ω
VT = 12 V
I2
I3
IT
1.3 Combination of Resistors in Series and
Resistors in Parallel.
Based on the formula: VT = V1 + V2
V2 = VT – V1 where V1 = IT X R1
In order to calculate IT, it is necessary to find the
value of the total resistance RT since IT = VT ÷
RT
RT = R1 + RP = (6 + 3.33) Ω = 9.33 Ω
I1
R2 = 5Ω
R1 = 6Ω
V1 V2
A

10. Where RP = Total Resistance in the parallel
branch.
IT = 12V/9.33 Ω = 1.286 A
Thus V1 = 1.286 A X 6 Ω = 7.717 V
Now going back to our formula for V2:
V2 = VT – V1 = (12 - 7.717 )V = 4.283 V
Calculating I2 and I3:
The voltage across each of the branches are the
same . V2 = I2 X R2 = I3 X R3
I2 = 4.283V ÷ 5 Ω = 0.857 A and
I3 = 4.283V ÷ 10 Ω = 0.428 A.

11. We can confirm our answer by adding up the
current at node A:
IT = I2 + I3
0.857 A + 0.428 A = 1.2853 A