1. Kirchoff’s Voltage & current laws
T. Elsarnagawy, mde 207, semester 311, rcc

2. T. Elsarnagawy, mde 207, semester 311, rcc
Kirchhoff’s voltage law
T. Elsarnagawy, mde 207, semester 311, rcc

3. T. Elsarnagawy, mde 207, semester 311, rcc
Kirchhoff’s voltage law
is generally stated as:
The sum of all the voltage drops around a single closed path in a circuit is equal to the total source voltage in that closed path.
KVL applies to all circuits, but you must apply it to only one closed path. In a series circuit, this is (of course) the entire circuit.
T. Elsarnagawy, mde 207, semester 311, rcc

4. T. Elsarnagawy, mde 207, semester 311, rcc
Kirchhoff’s voltage law
Notice in this series example that the sum of the resistor voltages is equal to the source voltage.
I1= R1= 0.68 kW V1= P1=
2.74 mA
1.86 V
5.1 mW
I2= R2= 1.50 kW V2= P2=
2.74 mA
4.11 V
11.3 mW
I3= R3= 2.20 kW V3= P3=
2.74 mA
6.03 V
16.5 mW
IT= RT= 4.38 kW VS= 12 V PT=
2.74 mA
32.9 mW
T. Elsarnagawy, mde 207, semester 311, rcc

5. T. Elsarnagawy, mde 207, semester 311, rcc

6. T. Elsarnagawy, mde 207, semester 311, rcc

7. T. Elsarnagawy, mde 207, semester 311, rcc
Voltage divider
T. Elsarnagawy, mde 207, semester 311, rcc

8. Two resistor voltage divider
The two resistor voltage divider is used often to supply a voltage different from that of an available battery or power supply.
In application the output voltage depends upon the resistance of the load it drives.
T. Elsarnagawy, mde 207, semester 311, rcc

9. T. Elsarnagawy, mde 207, semester 311, rcc
Voltage divider rule
The voltage drop across any given resistor in a series circuit is equal to the ratio of that resistor to the total resistance, multiplied by source voltage.
Assume R1 is twice the size of R2. What is the voltage across R1?
Question:
8 V
T. Elsarnagawy, mde 207, semester 311, rcc

10. T. Elsarnagawy, mde 207, semester 311, rcc
Voltage divider
Example:
What is the voltage across R2?
Solution:
Notice that 40% of the source voltage is across R2, which represents 40% of the total resistance.
The total resistance is 25 kW.
Applying the voltage divider formula:
T. Elsarnagawy, mde 207, semester 311, rcc

11. T. Elsarnagawy, mde 207, semester 311, rcc
Voltage divider
Voltage dividers can be set up for a variable output using a potentiometer. In the circuit shown, the output voltage is variable.
Question:
What is the largest output voltage available?
5.0 V
T. Elsarnagawy, mde 207, semester 311, rcc

12. T. Elsarnagawy, mde 207, semester 311, rcc
where is the parallel resistance of R2 and the load resistor RL.
T. Elsarnagawy, mde 207, semester 311, rcc

13. T. Elsarnagawy, mde 207, semester 311, rcc
Power in Series Circuits
Example:
Use the voltage divider rule to find V1 and V2. Then find the power in R1 and R2 and PT.
Solution:
Applying the voltage divider rule:
The power dissipated by each resistor is:
P=V2/R
PT = 0.5 W }
T. Elsarnagawy, mde 207, semester 311, rcc

14. T. Elsarnagawy, mde 207, semester 311, rcc
Circuit Ground
The term “ground” typically means a common or reference point in the circuit.
Voltages that are given with respect to ground are shown with a single subscript. For example, VA means the voltage at point A with respect to ground. VB means the voltage at point B with respect to ground. VAB means the voltage between points A and B.
Question:
What are VA, VB, and VAB for the circuit shown?
VA = 12 V
VB = 8 V
VAB = 4 V
T. Elsarnagawy, mde 207, semester 311, rcc

15. Kirchhoff’s current law
T. Elsarnagawy, mde 207, semester 311, rcc
T. Elsarnagawy, mde 207, semester 311, rcc

16. T. Elsarnagawy, mde 207, semester 311, rcc
Kirchhoff’s current law
is generally stated as:
The sum of the currents entering a node is equal to the sum of the currents leaving the node.
Notice in the previous example that the current from the source is equal to the sum of the branch currents.
I1= R1= 0.68 kW V1= P1=
I2= R2= 1.50 kW V2= P2=
I3= R3= 2.20 kW V3= P3=
IT= RT= 386 W VS= 5.0 V PT=
5.0 V
13.0 mA
2.3 mA
3.3 mA
7.4 mA
36.8 mW
16.7 mW
11.4 mW
64.8 mW
T. Elsarnagawy, mde 207, semester 311, rcc

17. T. Elsarnagawy, mde 207, semester 311, rcc
Special case for resistance of two parallel resistors
The resistance of two parallel resistors can be found by
either: or
Question:
What is the total resistance if R1 = 27 kW and R2 = 56 kW?
18.2 kW
T. Elsarnagawy, mde 207, semester 311, rcc

18. T. Elsarnagawy, mde 207, semester 311, rcc
Parallel current sources
Current sources in parallel can be combined algebraically into a single equivalent source.
The two current sources shown are aiding, so the net current in the resistor is their sum (2.5 mA).
Question:
(a) What is the current in R if the 1.5 mA source is reversed?
0.5 mA
(b) Which end of R will be positive?
The bottom
T. Elsarnagawy, mde 207, semester 311, rcc

19. T. Elsarnagawy, mde 207, semester 311, rcc

20. T. Elsarnagawy, mde 207, semester 311, rcc
Current divider
When current enters a junction it divides with current values that are inversely proportional to the resistance values.
and
The most widely used formula for the current divider is the two-resistor equation. For resistors R1 and R2,
Notice the subscripts. The resistor in the numerator is not the same as the one for which current is found.
T. Elsarnagawy, mde 207, semester 311, rcc

21. T. Elsarnagawy, mde 207, semester 311, rcc
Power in parallel circuits
Power in each resistor can be calculated with any of the standard power formulas. Most of the time, the voltage is
known, so the equation
is most convenient.
As in the series case, the total power is the sum of the powers dissipated in each resistor.
Homework
What is the total power if 10 V is applied to the parallel combination of R1 = 270 W and R2 = 150 W?
1.04 W
T. Elsarnagawy, mde 207, semester 311, rcc

22. T. Elsarnagawy, mde 207, semester 311, rcc
Key Terms
One current path in a parallel circuit.
Branch
Current divider
Junction
Kirchhoff’s current law
Parallel
A parallel circuit in which the currents divide inversely proportional to the parallel branch resistances.
A point at which two or more components are connected. Also known as a node.
A law stating the total current into a junction equals the total current out of the junction.
The relationship in electric circuits in which two or more current paths are connected between two separate points (nodes).
T. Elsarnagawy, mde 207, semester 311, rcc

23. T. Elsarnagawy, mde 207, semester 311, rcc
Key Terms
Circuit ground
Kirchhoff’s voltage law
Open
A method of grounding whereby the metal chassis that houses the assembly or a large conductive area on a printed circuit board is used as a common or reference point; also called chassis ground.
A law stating that (1) the sum of the voltage drops around a closed loop equals the source voltage in that loop or (2) the algebraic sum of all of the voltages (drops and source) is zero.
A circuit condition in which the current path is broken.
T. Elsarnagawy, mde 207, semester 311, rcc