Transcript Unit 8 Combination Circuits

Unit 8 Combination Circuits
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Objectives:
Define a combination circuit.
List the rules for parallel circuits.
List the rules for series circuits.
Solve for combination circuit values.
Unit 8 Combination Circuits
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Characteristics
There are multiple current paths.
Resistors may be in series or parallel with
other resistors.
A node is where three or more paths come
together.
The total power is the sum of the resistors’
power.
Unit 8 Combination Circuits
A simple combination circuit.
Unit 8 Combination Circuits
Solving Combination Circuits
E=?V
I=1A
R=?Ω
E1 = ? V
I1 = ? A
R1 = 325 Ω
E3 = ? V
I3 = ? A
R3 = 150 Ω
E2 = ? V
I2 = ? A
R2 = 275 Ω
E4 = ? V
I4 = ? A
R4 = 250 Ω
Unit 8 Combination Circuits
Series Circuit Rules
1. The current is the same at any point in
the circuit.
2. The total resistance is the sum of the
individual resistances.
3. The sum of the voltage drops or the
individual resistors must equal the
applied (source) voltage.
Unit 8 Combination Circuits
Parallel Circuit Rules
1. The voltage across any circuit branch is
the same as the applied (source)
voltage.
2. The total current is the sum of the current
through all of the circuit branches.
3. The total resistance is equal to the
reciprocal of the sum of the reciprocals of
the branch resistances.
Unit 8 Combination Circuits
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Simplifying the Circuit
Resistors in series can be combined to
form an equivalent resistance.
Resistors in parallel can be combined to
form an equivalent resistance.
The equivalent resistances are used to
draw simplified equivalent circuits.
Unit 8 Combination Circuits
Reducing Combination Circuits
Combine R1 & R2, and R3 & R4.
R1 = 325 Ω
R3 = 150 Ω
R2 = 275 Ω
R4 = 250 Ω
R=?Ω
Unit 8 Combination Circuits
Reducing Combination Circuits
Redraw simplified circuit.
R1 + R2 = R1&2 = 600 ohms
R3 + R4 = R3&4 = 400 ohms
R=?Ω
R1&2 = 600 Ω
R3&4 = 400 Ω
Unit 8 Combination Circuits
Solving Combination Circuits
Solve for the applied voltage using Ohm’s law.
Note that the I(total) was given data.
E(source) = I(total) x R(total) = 1 x 240 = 240 V
E = 240 V
I=1A
R = 240 Ω
R1&2 = 600 Ω
R3&4 = 400 Ω
Unit 8 Combination Circuits
Solving Combination Circuits
Solve for the branch currents using Ohm’s law.
E(source) = E1&2 = E3&4
I1&2 = E1&2 / R1&2 = 240/600 = 0.4 A
E = 240 V
I=1A
R = 240 Ω
E = 240 V
I = 0.4 A
R1&2 = 600 Ω
R3&4 = 400 Ω
Unit 8 Combination Circuits
Solving Combination Circuits
Solve for the branch currents using Ohm’s law.
E(source) = E1&2 = E3&4
I3&4 = E3&4 / R3&4 = 240/400 = 0.6 A
E = 240 V
I=1A
R = 240 Ω
E1&2 = 240 V
I = 0.4 A
R1&2 = 600 Ω
E3&4 = 240 V
I = 0.6 A
R3&4 = 400 Ω
Unit 8 Combination Circuits
Solving Combination Circuits
Expand the circuit back to the original circuit.
Branch currents remain the same.
E = 240 V
I=1A
R = 240 Ω
E1 = ? V
I1 = 0.4 A
R1 = 240 Ω
E3 = ? V
I3 = 0.6 A
R3 = 240 Ω
E2 = ? V
I2 = 0.4 A
R2 = 240 Ω
E4 = ? V
I4 = 0.6 A
R4 = 240 Ω
Unit 8 Combination Circuits
Solving Combination Circuits
Solve for each voltage drop using Ohm’s law.
E1 = I1 x R1 = 0.4 x 325 = 130 V
E = 240 V
I=1A
R = 240 Ω
E1 = 130 V
I1 = 0.4 A
R1 = 325 Ω
E3 = ? V
I3 = 0.6 A
R3 = 150 Ω
E2 = ? V
I2 = 0.4 A
R2 = 275 Ω
E4 = ? V
I4 = 0.6 A
R4 = 250 Ω
Unit 8 Combination Circuits
Solving Combination Circuits
Solve for each voltage drop using Ohm’s law.
E2 = I2 x R2 = 0.4 x 275 = 110 V
E = 240 V
I=1A
R = 240 Ω
E1 = 130 V
I1 = 0.4 A
R1 = 325 Ω
E3 = ? V
I3 = 0.6 A
R3 = 150 Ω
E2 = 110 V
I2 = 0.4 A
R2 = 275 Ω
E4 = ? V
I4 = 0.6 A
R4 = 250 Ω
Unit 8 Combination Circuits
Solving Combination Circuits
Solve for each voltage drop using Ohm’s law.
E3 = I3 x R3 = 0.6 x 150 = 90 V
E = 240 V
I=1A
R = 240 Ω
E1 = 130 V
I1 = 0.4 A
R1 = 325 Ω
E3 = 90 V
I3 = 0.6 A
R3 = 150 Ω
E2 = 110 V
I2 = 0.4 A
R2 = 275 Ω
E4 = ? V
I4 = 0.6 A
R4 = 250 Ω
Unit 8 Combination Circuits
Solving Combination Circuits
Solve for each voltage drop using Ohm’s law.
E4 = I4 x R4 = 0.6 x 250 = 150 V
E = 240 V
I=1A
R = 240 Ω
E1 = 130 V
I1 = 0.4 A
R1 = 325 Ω
E3 = 90 V
I 3= 0.6 A
R3 = 150 Ω
E2 = 110 V
I2 = 0.4 A
R2 = 275 Ω
E4= 150 V
I4 = 0.6 A
R4 = 250 Ω
Unit 8 Combination Circuits
Kirchhoff’s Laws
1. The algebraic sum of the voltage sources
and voltage drops in a closed circuit must
equal zero. This law states that the sum of
the voltage drops in a series circuit must
equal the applied voltage.
2. The algebraic sum of the current entering
and leaving a point must equal zero. The
second law is for parallel circuits and states
that the total current is the sum of all the
branch currents.
Unit 8 Combination Circuits
Solving Combination Circuits Review
E=?V
I=1A
R=?Ω
E1 = ? V
I1 = ? A
R1 = 325 Ω
E3 = ? V
I3 = ? A
R3 = 150 Ω
E2 = ? V
I2 = ? A
R2 = 275 Ω
E4 = ? V
I4 = ? A
R4 = 250 Ω
Unit 8 Combination Circuits
Solving Combination Circuits Review:
Combine R1 & R2, and R3 & R4
R1 = 325 Ω
R3 = 150 Ω
R2 = 275 Ω
R4 = 250 Ω
R=?Ω
Unit 8 Combination Circuits
Solving Combination Circuits Review:
Redraw simplified circuit.
R1 + R2 = R1&2 = 600 ohms
R3 + R4 = R3&4 = 400 ohms
R=?Ω
R1&2 = 600 Ω
R3&4 = 400 Ω
Unit 8 Combination Circuits
Solving Combination Circuits Review:
Solve for the applied voltage using Ohm’s Law.
Note that the I(total) was given data.
E(source) = I(total) x R(total) = 1 x 240 = 240 V
E = 240 V
I=1A
R = 240 Ω
R1&2 = 600 Ω
R3&4 = 400 Ω
Unit 8 Combination Circuits
Solving Combination Circuits Review:
Solve for the branch currents using Ohm’s law.
E(source) = E1&2 = E3&4
I1&2 = E1&2 / R1&2 = 240/600 = 0.4 A
E = 240 V
I=1A
R = 240 Ω
E = 240 V
I = 0.4 A
R1&2 = 600 Ω
R3&4 = 400 Ω
Unit 8 Combination Circuits
Solving Combination Circuits Review:
Solve for the branch currents using Ohm’s law.
E(source) = E1&2 = E3&4
I3&4 = E3&4 / R3&4 = 240/400 = 0.6 A
E = 240 V
I=1A
R = 240 Ω
E1&2 = 240 V
I = 0.4 A
R1&2 = 600 Ω
E3&4 = 240 V
I = 0.6 A
R3&4 = 400 Ω
Unit 8 Combination Circuits
Solving Combination Circuits Review:
Expand the circuit back to the original circuit.
Branch currents remain the same.
E = 240 V
I=1A
R = 240 Ω
E1 = ? V
I1 = 0.4 A
R1 = 240 Ω
E3 = ? V
I3 = 0.6 A
R3 = 240 Ω
E2 = ? V
I2 = 0.4 A
R2 = 240 Ω
E4 = ? V
I4 = 0.6 A
R4 = 240 Ω
Unit 8 Combination Circuits
Solving Combination Circuits Review:
Solve for each voltage drop using Ohm’s law.
E1 = I1 x R1 = 0.4 x 325 = 130 V
E = 240 V
I=1A
R = 240 Ω
E1 = 130 V
I1= 0.4 A
R1 = 325 Ω
E3 = ? V
I3 = 0.6 A
R3 = 150 Ω
E2 = ? V
I2 = 0.4 A
R2 = 275 Ω
E4 = ? V
I4 = 0.6 A
R4 = 250 Ω
Unit 8 Combination Circuits
Solving Combination Circuits Review:
Solve for each voltage drop using Ohm’s law.
E2 = I2 x R2 = 0.4 x 275 = 110 V
E = 240 V
I=1A
R = 240 Ω
E1 = 130 V
I1 = 0.4 A
R1 = 325 Ω
E3 = ? V
I3 = 0.6 A
R3 = 150 Ω
E2 = 110 V
I2 = 0.4 A
R2 = 275 Ω
E4 = ? V
I4 = 0.6 A
R4 = 250 Ω
Unit 8 Combination Circuits
Solving Combination Circuits Review:
Solve for each voltage drop using Ohm’s law.
E3 = I3 x R3 = 0.6 x 150 = 90 V
E = 240 V
I=1A
R = 240 Ω
E1 = 130 V
I1= 0.4 A
R1 = 325 Ω
E3 = 90 V
I3 = 0.6 A
R3 = 150 Ω
E2 = 110 V
I2 = 0.4 A
R2 = 275 Ω
E4 = ? V
I4 = 0.6 A
R4 = 250 Ω
Unit 8 Combination Circuits
Solving Combination Circuits Review:
Solve for each voltage drop using Ohm’s law.
E4 = I4 x R4 = 0.6 x 250 = 150 V
E = 240 V
I=1A
R = 240 Ω
E1 = 130 V
I1= 0.4 A
R1 = 325 Ω
E3 = 90 V
I3 = 0.6 A
R3 = 150 Ω
E2 = 110 V
I2 = 0.4 A
R2 = 275 Ω
E4 = 150 V
I4 = 0.6 A
R4 = 250 Ω
Unit 8 Combination Circuits
Review:
1. The three rules for series circuits are:
a. The current is the same at any point in
the circuit.
b. The total resistance is the sum of the
individual resistances.
c. The applied voltage is equal to the sum
of the voltage drops across the individual
components.
Unit 8 Combination Circuits
Review:
2. The three rules for parallel circuits are:
a. The total voltage is the same as the
voltage across any branch.
b. The total current is the sum of the
individual currents.
c. The total resistance is the reciprocal of
the sum of the reciprocals of the branch
resistances.
Unit 8 Combination Circuits
Review:
3. Combination circuits are circuits that
contain both series and parallel branches.
4. A node is where three or more paths come
together.
5. The total power is the sum of all the circuit
resistors’ power.
Unit 8 Combination Circuits
Review:
6. When solving combination circuits, simplify,
reduce, and redraw equivalent value
circuits.
7. Apply the series rules and the parallel rules
selectively to various parts of the
combination circuit.