# NCCER Elc L1/M4 MIX

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1. ### Slide 2 - Objectives

• When trainees have completed this lesson, they should be able to do the following:
• 1. Explain the basic characteristics of combination circuits.
• 2. Calculate, using Kirchhoff’s voltage law, the voltage drop in series, parallel, and series-parallel circuits.
• 3. Calculate, using Kirchhoff’s current law, the total current in parallel and series-parallel circuits.
• 4. Using Ohm’s law, find the unknown parameters in series, parallel, and series-parallel circuits.
• This is a knowledge-based module; there are no Performance Tasks.
• Electrical Theory 26104-14
2. ### Slide 3 - 1.0.0 – 2.1.0

• Electrical Theory 26104-14
• Introduction; Resistive Circuits
• • A series circuit contains only one path for current flow.
• • In a series circuit, the current is equal at each point in the circuit.
3. ### Slide 4 - 1.0.0 – 2.1.0

• Electrical Theory 26104-14
• Total Resistance
• • In a series circuit, the total resistance is equal to the sum of the individual resistances.
• • In the circuits shown here, the total resistance is:
• Circuit A, 50Ω + 75Ω + 100Ω = 225Ω
• Circuit B, 20Ω + 40Ω + 60Ω = 120Ω
4. ### Slide 5 - 2.2.0 – 2.1.0

• Electrical Theory 26104-14
• Resistances in Parallel
• • In a parallel circuit, the resistance is calculated by dividing the sum of the inverse values of the individual resistances by one:
• • In the circuit shown, the total resistance is :
5. ### Slide 6 - 2.2.1

• Electrical Theory 26104-14
• Simplified Formulas
• • The total resistance of equal resistors in parallel is found by dividing the resistance of each resistor by the number of resistors (RT = R/N).
• • The total resistance of two unequal resistors in parallel is found by multiplying the values of the two resistors and then dividing the sum of the two resistances:
6. ### Slide 7 - 2.3.0

• Electrical Theory 26104-14
• Series-Parallel Circuits
• • If a circuit does not divide, it is a series circuit.
• • If a circuit divides into separate branches, it is a parallel circuit.
• • If a circuit divides into separate branches and there are also series loads, it is a series-parallel circuit.
7. ### Slide 8 - 2.3.0

• Electrical Theory 26104-14
• Redrawing a Series-Parallel Circuit
• Series-parallel circuits can be redrawn to separate the series and parallel components.
8. ### Slide 9 - 2.3.0

• Electrical Theory 26104-14
• Reducing Series-Parallel Circuits
• To calculate the total resistance in a series-parallel circuit, first calculate the effective resistance of the parallel component, then add it to the resistance of the series loads.
• Next Session…
• Applying Ohm’s Law
9. ### Slide 10 - 2.4.0 – 2.4.1

• Electrical Theory 26104-14
• Applying Ohm’s Law
• • To find the voltage across individual resistors, first calculate the total resistance in the circuit.
• • Next, use the total resistance in the Ohm’s Law equation (E = IR) to find the individual voltage drops.
10. ### Slide 11 - 2.4.2

• Electrical Theory 26104-14
• Voltage and Current in Parallel Circuits
• • In a parallel circuit, the total current is equal to the sum of the branch currents.
• • The branch current is equal to the applied voltage divided by the resistance of that branch.
11. ### Slide 12 - 2.4.2

• Electrical Theory 26104-14
• Solving for an Unknown Current
• • The current in branch R2 in Circuit A can be calculated as follows:
• IT = I1 + I2
• • Rearrange to find I2:
• I2 = IT – I1
• I2 = 20A – 12A = 8A
• • The current in branch R1 in Circuit B can be calculated as follows:
• IT = I1 + I2
• • Rearrange to find I1:
• I1 = IT – I2
• I1 = 35A – 20A = 15A
12. ### Slide 13 - 2.4.3

• Electrical Theory 26104-14
• Voltage and Current in Series-Parallel Circuits
• • The series resistance is found by adding R1 + R2:
• R1+2 = R1 + R2
• R1+2 = 0.5kΩ + 0.5kΩ
• R1+2 = 1kΩ
• • Calculate the resistance of R3 + R4 using either the general reciprocal formula or the product over sum method, as shown here:
13. ### Slide 14 - 2.4.3

• Electrical Theory 26104-14
• Simplified Series-Parallel Circuit
• • Calculate the total resistance as follows:
• RT = R1+2 + R3+4
• RT = 1kΩ + 0.5kΩ = 1.5kΩ
• • Apply this in Ohm’s law to find the total current as follows:
• IT = ET/RT
• IT = 1.5V/1.5kΩ = 1mA or 0.001A
• • Individual voltage drops are calculated using Ohm’s law:
• ER1 = ITR1 = 1mA x 0.5kΩ = 0.5V
• ER2 = ITR2 = 1mA x 0.5kΩ = 0.5V
• Next Session…
• Kirchhoff’s Laws
14. ### Slide 15 - 3.0.0 – 3.1.0

• Electrical Theory 26104-14
• Kirchhoff’s Laws
• • Kirchhoff’s current law states that at any point in a circuit, the total current entering that point must equal the total current leaving that point:
• IA + IB – IC = 0
• 5A + 3A – 8A = 0
• • Kirchhoff’s current law is the basis for the practical rule in parallel circuits that the total line current must equal the sum of the branch currents.
15. ### Slide 16 - 3.0.0 – 3.1.0

• Electrical Theory 26104-14
• Application of Kirchhoff’s Current Law
• • Applying Kirchhoff’s current law to this circuit at Point C can be shown as follows:
• IT – I3 – I4/5 = 0
• 6A – 2A – 4A = 0
• • Applying Kirchhoff’s current law to this circuit at Point D can be shown as follows:
• I3 + I4/5 – IT = 0
• A + 4A – 6A = 0
16. ### Slide 17 - 3.2.0

• Electrical Theory 26104-14
• Kirchhoff’s Voltage Law
• • Kirchhoff’s voltage law states that the algebraic sum of all the potential differences in a closed loop is equal to zero:
• EA – E1 – E2 – E3 = 0
• 100A – 50A – 30A – 20A = 0
• • This means that the sum of the voltage drops in a circuit is equal to the applied voltage.
17. ### Slide 18 - 3.3.0

• Electrical Theory 26104-14
• Loop Equations
• • Any closed path for current flow is called a loop. A loop equation specifies the voltages around the loop:
• – E1 – E3 – E2 + ET = 0
• – 30V – 120V – 90V + 240V = 0
• • Voltages E1, E3, and E2 have a negative value because there is a decrease in voltage seen across each of these resistors in a clockwise direction.
18. ### Slide 19 - 3.3.0

• Electrical Theory 26104-14
• Applying Kirchhoff’s Voltage Law
• The voltage EB is calculated as follows:
• – E3 – EB – E2 – E1 + EA = 0
• Rearranged to solve for EB:
• EB = EA – E3 – E2 – E1
• EB = 15V – 2V – 6V – 3V
• EB = 4V
19. ### Slide 20 - Wrap Up

• 3-2-1
• 3 – Write 3 important things learned during class
• 2 – Write 2 questions you have about the material