NCCER Elc L1/M4 MIX

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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 seriesparallel circuits.
 3. Calculate, using Kirchhoff’s current law, the total current in parallel and seriesparallel circuits.
 4. Using Ohm’s law, find the unknown parameters in series, parallel, and seriesparallel circuits.
 This is a knowledgebased module; there are no Performance Tasks.
 Electrical Theory 2610414

Slide 3  1.0.0 – 2.1.0
 Electrical Theory 2610414
 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.

Slide 4  1.0.0 – 2.1.0
 Electrical Theory 2610414
 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

Slide 5  2.2.0 – 2.1.0
 Electrical Theory 2610414
 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 :

Slide 6  2.2.1
 Electrical Theory 2610414
 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:

Slide 7  2.3.0
 Electrical Theory 2610414
 SeriesParallel 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 seriesparallel circuit.

Slide 8  2.3.0
 Electrical Theory 2610414
 Redrawing a SeriesParallel Circuit
 Seriesparallel circuits can be redrawn to separate the series and parallel components.

Slide 9  2.3.0
 Electrical Theory 2610414
 Reducing SeriesParallel Circuits
 To calculate the total resistance in a seriesparallel 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

Slide 10  2.4.0 – 2.4.1
 Electrical Theory 2610414
 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.

Slide 11  2.4.2
 Electrical Theory 2610414
 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.

Slide 12  2.4.2
 Electrical Theory 2610414
 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

Slide 13  2.4.3
 Electrical Theory 2610414
 Voltage and Current in SeriesParallel 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:

Slide 14  2.4.3
 Electrical Theory 2610414
 Simplified SeriesParallel 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

Slide 15  3.0.0 – 3.1.0
 Electrical Theory 2610414
 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.

Slide 16  3.0.0 – 3.1.0
 Electrical Theory 2610414
 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

Slide 17  3.2.0
 Electrical Theory 2610414
 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.

Slide 18  3.3.0
 Electrical Theory 2610414
 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.

Slide 19  3.3.0
 Electrical Theory 2610414
 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

Slide 20  Wrap Up
 321
 3 – Write 3 important things learned during class
 2 – Write 2 questions you have about the material
 1 – Write 1 thought you had about the material
 Electrical Theory 2610414

Slide 21  Next Session…
 MODULE EXAM
 Review the complete module to prepare for the module exam. Complete the Module Review as a study aid.
 Electrical Theory 2610414