4.3.b form 4 combined circuits

Unit 8

Combination Circuits

Unit 8 Combination Circuits

Objectives:

• Define a combination circuit.

• List the rules for parallel circuits.

• List the rules for series circuits.

• Solve for combination circuit values.


Characteristics

• There are multiple current paths.

• Resistors may be in series or parallel with other resistors.

• A junction is where three or more paths come together.

• The total power is the sum of the resistors’ power.


A simple combination circuit.


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.


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.


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.


Solving Combination Circuits

E = ? V

I = 1 A

R = ? Ω

E1 = ? V

I1 = ? A

R1 = 325 Ω

E2 = ? V

I2 = ? A

R2 = 275 Ω

E3 = ? V

I3 = ? A

R3 = 150 Ω

E4 = ? V

I4 = ? A

R4 = 250 Ω


Reducing Combination Circuits

Combine R1 & R2, and R3 & R4.

R = ? Ω

R1 = 325 Ω

R2 = 275 Ω

R3 = 150 Ω

R4 = 250 Ω


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

Calculate total resistance



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 = 1 A

R = 240 Ω

R1&2 = 600 Ω R3&4 = 400 Ω



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 = 1 A

R = 240 Ω

E = 240 V

I = 0.4 A

R1&2 = 600 Ω

R3&4 = 400 Ω



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 = 1 A

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



Expand the circuit back to the original circuit.

Branch currents remain the same.

E = 240 V

I = 1 A

R = 240 Ω

E1 = ? V

I1 = 0.4 A

R1 = 240 Ω

E2 = ? V

I2 = 0.4 A

R2 = 240 Ω

E3 = ? V

I3 = 0.6 A

R3 = 240 Ω

E4 = ? V

I4 = 0.6 A

R4 = 240 Ω



Solve for each voltage drop using Ohm’s law.

E1 = I1 x R1 = 0.4 x 325 = 130 V

E = 240 V

I = 1 A

R = 240 Ω

E1 = 130 V

I1 = 0.4 A

R1 = 325 Ω

E2 = ? V

I2 = 0.4 A

R2 = 275 Ω

E3 = ? V

I3 = 0.6 A

R3 = 150 Ω

E4 = ? V

I4 = 0.6 A

R4 = 250 Ω




E2 = I2 x R2 = 0.4 x 275 = 110 V

E = 240 V

I = 1 A

R = 240 Ω

E1 = 130 V

I1 = 0.4 A

R1 = 325 Ω

E2 = 110 V

I2 = 0.4 A

R2 = 275 Ω

E3 = ? V

I3 = 0.6 A

R3 = 150 Ω

E4 = ? V

I4 = 0.6 A

R4 = 250 Ω




E3 = I3 x R3 = 0.6 x 150 = 90 V

E = 240 V

I = 1 A

R = 240 Ω

E1 = 130 V

I1 = 0.4 A

R1 = 325 Ω

E2 = 110 V

I2 = 0.4 A

R2 = 275 Ω

E3 = 90 V

I3 = 0.6 A

R3 = 150 Ω

E4 = ? V

I4 = 0.6 A

R4 = 250 Ω




E4 = I4 x R4 = 0.6 x 250 = 150 V

E = 240 V

I = 1 A

R = 240 Ω

E1 = 130 V

I1 = 0.4 A

R1 = 325 Ω

E2 = 110 V

I2 = 0.4 A

R2 = 275 Ω

E3 = 90 V

I 3= 0.6 A

R3 = 150 Ω

E4= 150 V

I4 = 0.6 A

R4 = 250 Ω


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.


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.


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.


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.

4.3.b form 4 combined circuits

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