Lecture 4 (Week 4)

1.

Series - Parallel Circuits
OEk 1115 - Fundamentals of Electronics
Lecture 4

2.

Outline
Series-Parallel Circuits
Total Resistance
Total Current
Branch Currents
Voltage Relationships
Load Current and Bleeder Current

3.

Series - Parallel Circuits
A series-parallel circuit consists of combinations of both series and parallel
current paths.
It is important to be able to identify how the components in a circuit are arranged
in terms of their series and parallel relationships.

4.

Series - Parallel Circuits

5.

Series - Parallel Circuits

6.

Series - Parallel Circuits

7.

Series - Parallel Circuits
Example. Identify the series-parallel relationships.

8.

Series - Parallel Circuits
Solution.

9.

Series - Parallel Circuits
Example. Describe the series-parallel combination between terminals A and D.

10.

Series - Parallel Circuits
Solution.

11.

Series - Parallel Circuits
Example. Describe the total resistance between each pair of terminals.

12.

Series - Parallel Circuits
Solution.

13.

Series - Parallel Circuits
Example. Identify the series-parallel relationships.

14.

Series - Parallel Circuits
Solution.

15.

Analysis of Series-Parallel Resistive Circuits
The analysis of series-parallel circuits can be approached in many ways,
depending on what information you need and what circuit values you know.
If you know Ohm’s law, Kirchhoff’s laws, the voltage-divider formula, and the
current-divider formula, and if you know how to apply these laws, you can solve
most resistive circuit analysis problems.
The ability to recognize series and parallel combinations is, of course, essential.
There is no standard “cookbook” approach that can be applied to all situations.
Logical thought is the most powerful tool you can apply to problem solving.

16.

Total Resistance
To find the total resistance (RT) of a series-parallel combination,
1. identify the series and parallel relationships,
2. determine total series and total parallel resistance.

17.

Total Resistance
Example. Determine RT between terminals A and B of the circuit.

18.

Total Resistance
Solution.

19.

Total Resistance
Example. Find RT of the circuit.

20.

Total Resistance
Solution.

21.

Total Current
Once you know the total resistance and the source voltage, you can apply Ohm’s
law to find the total current in a circuit.
Example. Let’s find the total current in the circuit in last example. Assume that the
source voltage is 10 V. The calculation is

22.

Branch Currents
Using the current-divider formula, Kirchhoff’s current law, Ohm’s law, or
combinations of these, you can find the current in any branch of a series-parallel
circuit.
In some cases, it may take repeated application of the formula to find a given
current.

23.

Branch Currents
Example. Determine the current through R4 if Vs = 5 V.

24.

Branch Currents
Solution.

25.

Voltage Relationships

26.

Voltage Relationships
1. V(R1) and V(R2) are equal because R1 and R2 are in parallel.
2. V(R3) is equal to V(R4) + V(R5) because R3 is in parallel with the series
combination of R4 and R5.
3. V(R4) is about one-third of the voltage from B to C because R4 is about onethird of the resistance R4 + R5 (by the voltage-divider principle).
4. V(R5) is about two-thirds of the voltage from B to C because R5 is about twothirds of R4 + R5.
5. V(R1) + V(R3) - Vs = 0 because, by Kirchhoff’s voltage law, the algebraic sum
of the voltage drops around a single closed path must equal zero.

27.

Voltage Relationships
Example. Verify that the voltmeter readings in previous slide are correct. The
circuit is redrawn as a schematic.

28.

Solution.

29.

Voltage Relationships
Determine the voltage drop across each resistor in Figure

30.

Voltage Dividers with Resistive Loads
The voltage divider in circuit produces an output voltage (Vout). This voltage is the
unloaded output voltage.
When a load resistor, RL is connected from the output to ground the output voltage
is reduced by an amount that depends on the value of RL. This effect is called
loading.

31.

Voltage Dividers with Resistive Loads
Example.
a) Determine the unloaded output voltage of the voltage divider.
b) Find the loaded output voltages of the voltage divider for the following two
values of load resistance: RL = 10 kOhm and RL = 100 kOhm.

32.

Solution.

33.

Load Current and Bleeder Current
In a multiple-tap loaded voltage-divider circuit, the total current drawn from the
source consists of currents through the load resistors, called load currents, and
the divider resistors.
Bleeder current is a current left after the total load current is subtracted from the
total current in the circuit.

34.

Voltage Dividers with Resistive Loads
Example. Determine the load currents I(RL1)and and I(RL2) and the bleeder
current I3 in the two-tap loaded voltage divider.

35.

Voltage Dividers with Resistive Loads
Solution.

36.

Voltage Dividers with Resistive Loads
Solution.

37.

Voltage Dividers with Resistive Loads
Solution.

38.

Serial and Parallel
Find the total resistance between A and B in the circuit, current through R3, VR2,

39.

Serial and Parallel
Determine total resistance and total current in the circuit

40.

Serial and Parallel
Determine the total resistance and the voltage at points A, B, and C in the circuit

41.

Serial and Parallel
Determine the voltage at point A and B in the circuit

42.

Q&A
Any Questions?