AC Circuit Analysis (1)

Question 1

What are the equations AC voltage?

Note only considering cosine functions not sine

Answer 1

Note:
* The V is Vr.m.s value, which is multiplied by root(2) to then

Question 2

What are the key parameters that make up an AC Waveform?

Try to describe their equations and how they fit into the graph.

Answer 2

Note: phase is important. A negative phi refers to the wave moving towards the right, while positive is to the left.

Question 3

What are the two main AC voltage and Current equations?

Answer 3

Question 4

What are the main trigometeric identities that needs to be understood for AC waveforms?

Answer 4

Question 5

What are Root Mean Square (r.m.s) values? What are their equations?

Answer 5

What are they?
* r.m.s values are the equivalent DC voltage, V, or current, I, that generates the same average amount of power, P, in a resistor. This can be explained in the solution below.
* Note: The average power for AC can be seen to be almost equivalent to DC, where V in the DC circuit is equivalent to Vr.m.s

Question 6

True or False:

You can use KVL and KCL in AC circtuits to analyse them.

Answer 6

True! However:
* Because in AC circuits there is a time-domain in the circuit (i.e. t) in the equations. Then differential equations need to be solved, which provides both the transient and steady state solutions. However, this can be complex

Question 7

What are phasors? How are they useful?

Answer 7

• A phasor is a line drawn to represent a sinusoidal alternating quantity.
• Its length represents the magnitude, and its angle relative to the horizontal axis represents its phase shift. (So anti-clockwise round the phasor represents a positive angle and clockwise a negative angle).
• Example is shown below
• Phasors are normally fixed in position corresponding to t=0, to simplify its application in circuit analysis.
• Usually, the length of the phasor also represents r.m.s values.

Question 8

What is meant by ‘in phase’ and ‘differing in phase’? Consider the terms lag and leading.

Try to think about phasor addition and subtraction.

Answer 8

• In phase: both phasors are at the same angle and move at the same angular frequency.
• Out of phase/ differing in phase: one vector can be said to be lagging, or the other leading one another. There is now a phase difference between the two phasors.
• The phase difference between the two phasors can lead to subtraction or addition of the phasors for the output.

This can result in addition or subtraction of phasor voltages or currents as a result as shown below.

Question 9

Try to solve this question

Answer 9

Question 10

What is complex phasor notation? Why would we use it?

Answer 10

The reason it’s used?
* The phasor method can work but for complex circuits it can get difficult to analyse all the different components, angles and magnitudes.

Complex notation:
* This is just complex nototation shown below, in the various forms, which needs to be understood.
* Notice how a phasor diagram can be made into complex notation. Using real and imaginary graph and overalying it on the phasor notation diagram.
* An example of it being used is shown below.
* Notice how it is easier to add, subtract, divide and multiply the phasor circuits easier than before. Due to the complex notation.

Question 11

What are the three forms of complex numbers?

Answer 11

• Polar form
• Cartesian form
• Exponential form
• Conversions shown below

Question 12

How does summation of complex numbers work?

Try to think in the easiest form for it.

Answer 12

• Cartesian form is the easiest to sum

Question 13

How does subtraction of complex numbers work?

Try to think in the easiest form for it.

Answer 13

• Cartesian form is the easiest form for subtraction

Question 14

How does multiplicatoin of complex numbers work?

Try to think in the easiest form for it.

Answer 14

• Polar form is easiest for it.

Question 15

How does division of complex numbers work?

Try to think in the easiest form for it.

Answer 15

• Polar form is easiest for it.