1. DC Circuit Analysis Agenda Review - Characteristics of Resistors
Series/Parallel Circuits
Circuit Analysis by Circuit Reduction
Examples
Kirchhoff’s Theorems
Multiple Source Circuit Analysis using Kirchhoff’s Rules
Example
Quiz
Homework

2. DC Circuit Analysis Review Characteristics of Resistors
Resistor materials
Characteristics – Resistance, Tolerance, Power rating, Temp coef.
Examples of resistors
Resistors in Series:
Rule: The sum of the voltages around a closed circuit is Zero.
Therefore: V = V1 + V2 + V3 = IR1 + IR2 + IR3 = I(R1 + R2 + R3) Rs = V = R1 + R2 + R I
The Current Through each resistor is the Same.
The total resistance is always Greater than the largest resistor.

3. DC Circuit Analysis Review Resistors in Parallel:
Rule: The sum of the currents through all resistors equals the total current.
Therefore: I = I1 + I2 + I3 V/Rp = V/R1 + V/R2 + V/R3 = V(1/R1 + 1/R2 + 1/R3) 1/Rp = 1/R1 + 1/R2 + 1/R3
The Voltage across each resistor is the Same.
The Current Divides based on each resistance.
Total Resistance is always less than the smallest resistor.
For Two Resistors: Rp = R1xR R1+R2
For N equal resistors: Rp = R/N

4. Circuit Analysis by Reduction
DC Circuit Analysis
Circuit Analysis by Reduction
Calculate the Total current from the battery, the current through each resistor, and the voltage across each resistor.

5. Circuit Analysis by Reduction
DC Circuit Analysis
Circuit Analysis by Reduction
Calculate the Total current from the battery, the current through each resistor, and the voltage across each resistor.
Total current = 24v/8Ω = 3A VR1 = 3Ax6Ω = 18v VR2 = 24-18=6v IR2 = 6v/4Ω = 1.5A = IR5 VR5 = 1.5Ax2.5Ω = 3.75V VR3 = 6v-3.75v = 2.25v = VR4 IR3 = 2.25v/6Ω = 0.375A IR4 = 2.25v/2Ω = 1.125A

6. DC Circuits, Kirchhoff’s Law
DC Circuit Analysis
DC Circuits, Kirchhoff’s Law
For circuits that cannot be reduced by simple series/parallel methods, such as circuits with multiple voltage sources, we use Kirchhoff’s loop methods. These methods depend on two rules:
Rule 1: The algebraic sum of the currents at any junction is Zero. (Junction theorem)
Rule 2: The algebraic sum of the potential differences (voltages) across all of the elements of any closed loop is Zero. (loop theorem)
A Junction is a point at which three or more wires are joined.
Examples:
Junction
Junction
Define loops for analysis
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7. DC Circuits, Kirchhoff’s Law
DC Circuit Analysis
DC Circuits, Kirchhoff’s Law
Rule 1: The algebraic sum of the currents at any junction is Zero. (Junction theorem)
Rule 2: The algebraic sum of the potential differences (voltages) across all of the elements of any closed loop is Zero. (loop theorem)
Conventions: Battery: minus to plus is positive; Resistor: with assumed current flow is Negative. 6v
12v
R1=6Ω
R3=2Ω
R2=9Ω
1/13/2019

8. DC Circuits, Kirchhoff’s Law
DC Circuit Analysis
DC Circuits, Kirchhoff’s Law
Rule 1: The algebraic sum of the currents at any junction is Zero. (Junction theorem)
Rule 2: The algebraic sum of the potential differences (voltages) across all of the elements of any closed loop is Zero. (loop theorem)
Conventions: Battery: minus to plus is positive; Resistor: with assumed current flow is Negative. 6v
12v
R1=6Ω
R3=2Ω
R2=9Ω
1)Rule 1: I1 = I2 + I3
1/13/2019

9. DC Circuits, Kirchhoff’s Law
DC Circuit Analysis
DC Circuits, Kirchhoff’s Law
Rule 1: The algebraic sum of the currents at any junction is Zero. (Junction theorem)
Rule 2: The algebraic sum of the potential differences (voltages) across all of the elements of any closed loop is Zero. (loop theorem)
Conventions: Battery: minus to plus is positive; Resistor: with assumed current flow is Negative. 6v
12v
R1=6Ω
R3=2Ω
R2=9Ω
1)Rule 1: I1 = I2 + I3
2)Rule 2, loop 1: V1 – I1R1 – V2 – I3R3 = 0 = 6 – 6I1 -12 – 2I3 = 0 : 6I1 + 2I3 = -6 :
3I1 + I3 = -3
1/13/2019

10. DC Circuits, Kirchhoff’s Law
DC Circuit Analysis
DC Circuits, Kirchhoff’s Law
Rule 1: The algebraic sum of the currents at any junction is Zero. (Junction theorem)
Rule 2: The algebraic sum of the potential differences (voltages) across all of the elements of any closed loop is Zero. (loop theorem)
Conventions: Battery: minus to plus is positive; Resistor: with assumed current flow is Negative. 6v
12v
R1=6Ω
R3=2Ω
R2=9Ω
1)Rule 1: I1 = I2 + I3
2)Rule 2, loop 1: V1 – I1R1 – V2 – I3R3 = 0 = 6 – 6I1 -12 – 2I3 = 0 : 6I1 + 2I3 = -6 :
3I1 + I3 = -3
3)Rule 2, loop 2: V2 – I2R2 + I3R3 = 0 :
12 – 9I2 + 2I3 = 0 : 9I2 – 2I3 = 12 :
1/13/2019

11. DC Circuits, Kirchhoff’s Law
DC Circuit Analysis
DC Circuits, Kirchhoff’s Law
Rule 1: The algebraic sum of the currents at any junction is Zero. (Junction theorem)
Rule 2: The algebraic sum of the potential differences (voltages) across all of the elements of any closed loop is Zero. (loop theorem)
Conventions: Battery: minus to plus is positive; Resistor: with assumed current flow is Negative. 6v
12v
R1=6Ω
R3=2Ω
R2=9Ω
1)Rule 1: I1 = I2 + I3
2)Rule 2, loop 1: V1 – I1R1 – V2 – I3R3 = 0 = 6 – 6I1 -12 – 2I3 = 0 : 6I1 + 2I3 = -6 :
3I1 + I3 = -3
3)Rule 2, loop 2: V2 – I2R2 + I3R3 = 0 :
12 – 9I2 + 2I3 = 0 : 9I2 – 2I3 = 12 :
Combine 1 and 2 : 3(I2 + I3) + I3 = -3 :
3I2 + 4I3 = -3 : I2 = -1 – 4/3I3 :
1/13/2019

12. DC Circuits, Kirchhoff’s Law
DC Circuit Analysis
DC Circuits, Kirchhoff’s Law
Rule 1: The algebraic sum of the currents at any junction is Zero. (Junction theorem)
Rule 2: The algebraic sum of the potential differences (voltages) across all of the elements of any closed loop is Zero. (loop theorem)
Conventions: Battery: minus to plus is positive; Resistor: with assumed current flow is Negative. 6v
12v
R1=6Ω
R3=2Ω
R2=9Ω
1)Rule 1: I1 = I2 + I3
2)Rule 2, loop 1: V1 – I1R1 – V2 – I3R3 = 0 = 6 – 6I1 -12 – 2I3 = 0 : 6I1 + 2I3 = -6 :
3I1 + I3 = -3
3)Rule 2, loop 2: V2 – I2R2 + I3R3 = 0 :
12 – 9I2 + 2I3 = 0 : 9I2 – 2I3 = 12 :
Combine 1 and 2 : 3(I2 + I3) + I3 = -3 :
3I2 + 4I3 = -3 : I2 = -1 – 4/3I3 :
Sub into 3) : 9(-1 – 4/3I3) – 2I3 = 12 :
-14I3 = 21 : I3 = -1.5A : I2 = -1 -4/3 (-1.5A)
= 1.0A : I1 = I2 + I3 = 1.0 – 1.5A = -0.5A
Note: I3 and I1 are opposite assumed directions
1/13/2019

13. DC Circuit Analysis Quiz
Date ________
Name ____________
DC Circuit Analysis
Quiz
1) Draw a circuit diagram showing three resistors in Series:
2) Calculate the equivalent resistance of this circuit:
3) What is the voltage across resistor R2 in this circuit?
4) Extra credit: What is the current thru R2 ?

14. DC Circuit Analysis Homework
Date ________
Name ____________
DC Circuit Analysis
Homework
What is the equivalent resistance of this circuit?
For the circuit shown, find a) the current in each resistor, b) the voltage across each resistor and c) the total power delivered. (use the back side if you need more space)
Find the current in each resistor in the following circuit. (use the back side if you need more space)