1. Circuit Elements Voltage and current sources Electrical resistance
Kirchhoff’s Laws
Resistive Circuits

2. Voltage and current sources
An electrical source is a device that is capable of converting nonelectric energy to electric energy (and vice versa)
An ideal voltage source is a circuit element that maintains a prescribed voltage across its terminals regardless of current flowing in these terminals
An ideal current source is a circuit element that maintains a prescribed current across its terminals regardless of voltage across the terminals

3. Ideal voltage source
Current-voltage characteristic
Circuit symbol

4. Ideal current source
Current-voltage characteristic
Circuit symbol

5. Connections of ideal sources
Valid connections

6. Connections of ideal sources
Invalid connections

7. Connections of ideal sources
Valid or invalid?

8. Electrical resistance
Resistance is the capacity of materials to impede the flow of current
A resistor is a circuit element that displays this behavior
Current-voltage characteristic
Circuit symbol

9. Electrical resistance, cont.
Resistor’s obey Ohm’s Law:
V = I R
The voltage “drop” across a resistor is linearly proportional
to the current passing through the resistor

10. Electrical resistance, cont.
Example #1
I = V/R = 5V/1E3W = 5mA

11. Electrical resistance, cont.
Example #2
What is voltage drop across R1
What is voltage polarity?

12. Kirchhoff’s Laws
A node is a point in a circuit where two or more elements meet

13. Kirchhoff’s current law
The algebraic sum of all the currents
at any node in a curcuit equals zero
I1 + I2 + I3 = 0

14. Kirchhoff’s voltage law
The algebraic sum of all the voltages
around any closed path in a circuit equals zero
VR3 + VR1 + VR2
+ VC0 + VC4 = 0

15. Resistors in series Using KVL and KCL, we have: -V1 + I*R1 + I*R2 = 0
I*( ) = I = 30V/30W = 1A

16. Resistors in series Resistors in series add together
This is equivalent to:
Rs = R1 + R2
Resistors in series add together

17. Resistors in parallel Using KVL and KCL, we have:
V1 = I1R1 = I2R2 = 10V
I1 = 0.100A I2 = 0.033A
It = = 0.133A

18. Resistors in parallel Resistors in parallel are
This is equivalent to:
Resistors in parallel are
combined by adding their
reciprocals
1/Rp = 1/R1 + 1/R2

19. Classwork Find (a) the current through R3, (b) the current
through R2, and (c) voltage across R1