Topic 4: Equivalent Circuits and Superposition Principle

Question 1

What is a linear circuit?

Answer 1

A linear circuit is one that contains linear elements, independent sources and linear dependent sources.
Has the property:
Outputs are proportional to inputs.

Question 2

What is a linear element?

List examples of linear elements?

Answer 2

A linear element possesses a linear relationship between cause and effect. 
Examples include:
- resistors
- inductors 
- capacitors

Question 3

Give an example of the relationship between cause and effect in a linear element.

Answer 3

When a voltage is impressed across a resistor, the amount of resultant current (effect) is proportional to the voltage (cause).

Question 4

What is a linear dependent source?

Answer 4

The output voltage/ current proportional only to the first power of some current or voltage variable in the circuit (or a sum of such quantities).

Question 5

What does the superposition principle state?

Answer 5

Defined as a response in a linear circuit is equal to the sum of the responses for each independent source acting alone with the other independent source zeroed.

Question 6

How do you zero a voltage source?

Answer 6

To zero a voltage source, convert the source to a short circuit (V = 0)

Question 7

How do you zero a current source?

Answer 7

To zero a current source, convert the source to an open circuit (i = 0).

Question 8

What is the method for applying the superposition principle?

Answer 8

1. Zero all but 1 source and conduct circuit analysis.
2. Repeat step 1 until all sources have been analysed.
3. Sum the results of each of the individual sources to get the result for the whole circuit.

Question 9

What is an ideal voltage source?

Answer 9

A voltage source whose terminal voltage is independent of the current through it.
Ideal voltage sources do not exist in reality.

Question 10

How is a practical voltage source modelled?

Answer 10

Modelled with a resistor in series with an ideal voltage source.

Question 11

What is the equation for a practical voltage source?

Answer 11

v = vs - Rsv(i) 
where 
Rsv = internal/output resistance
vs = ideal voltage
i = output current

Question 12

What is an ideal current source?

Answer 12

A current source whose current independent of the voltage across it.

Question 13

How is a practical current source modelled?

Answer 13

Modelled with a resistor in parallel, with an ideal current source.

Question 14

What is the equation for a practical current source?

Answer 14

i = is - (V/(Rsi))

Question 15

What are the conditions under which a a practical voltage and current source are equivalent?

Answer 15

For a practical voltage source and a practical current source to be equivalent
Rsv = Rsi
and
vs = isRsi

Question 16

What does the process of source transformation allow for?

Answer 16

The process of source transformation simplifies a circuit solution by transforming voltage sources into current sources and vice versa.

Question 17

For superposition, can only one independent source be considered at a time?

Answer 17

No, any number of sources may be considered simultaneously.

Question 18

Can the superposition principle be applied to power calculations?

Answer 18

No, it cannot be applied to calculations.

Question 19

How do you calculate the Thevenin’s Equivalent Resistance?

Answer 19

Zero all sources and calculate the equivalent resistance. This is the Thevenin’s equivalent resistance.