AC Circuit Analysis (2)

Question 1

What are the equations for resistance, R, reactance, X, and impedance, Z, for a resistor, inductor and capacitor?

Use complex notation. Try to give values where you can.

Answer 1

Question 2

How do we work out Voltage for Resistors, Vr, Inductors, VL, and Capacitors, Vc, using complex notation, for AC circuits?

Answer 2

Question 3

What is the mnemonic to remeber what leads and lags (refering to current and voltage) in inductors and capacitors in AC circuits?

Answer 3

Question 4

Try to derive impedence of a resistor, Zr, from time domain form to complex phasor form.

Answer 4

Question 5

What is the current and voltage relationship for a Resistor in an AC circuit?

Think how to phasor looks and in terms of complex notation.

Answer 5

Question 6

Try to derive impedence of an Inductor, ZL, from time domain form to complex phasor form.

Answer 6

Note:
* We have to differentiate the expression and change the sine function back to cosine using trig identities
* The r.m.s voltage is equal to ωIL
* As the angular frequency, ω, increases, Inductive reactance, XL, increases, and vice versa.
* Note how ZL is derived from complex number form.
* See how j = e^(pi/2)

Question 7

What is the current and voltage relationship for an Inductor in an AC circuit?

Think how to phasor looks and in terms of complex notation.

Answer 7

Current lags voltage by 90 degrees or pi/2. Remember CIVIL

Question 8

Try to derive impedence of a capacitor, Zc, from time domain form to complex phasor form.

Answer 8

Note:
* we have to integrate the function, then convernt the sine function back into cosine function.
* The r.m.s Voltage is equal to ((1/ωC) x I)
* See how as angular frequency, ω, increases, capacitive reactance, Xc, decreases. And vice versa.
* Note how Zc is derived from complex form

Question 9

What is the current and voltage relationship for a Capacitor in an AC circuit?

Think how to phasor looks and in terms of complex notation.

Answer 9

Current leads voltage by 90 degrees, or pi/2.

Question 10

Have a go at this question:

Answer 10

Question 11

Why do we use complex phasor notation to analyse AC circuits?

Answer 11

Because in that form, we can analyse an AC circuit, similar to a DC circuit with ease.

Question 12

What is the difference between Reactance, X, and Impedence, Z?

Answer 12

• Reactance, X, is more of a measure of resistance of a component (like an inductor or capacitor) in an AC circuit.
• Impedence, Z, is a measure of the reactance and resistance combined in a components (like an inductor or capacitor). That is why it is taken into account in complex form as that accounts for sine and cosine functions.

Question 13

What are the general steps to analyse an AC circuit using complex phasors?

Answer 13

1. Replace the time domain forms of current and voltage with the complex phasor form.
2. Work out the impedence for R, L, and C’s in the circuit
3. Analyse the circuit like a DC circuit, using complex numbers