Semester 2

Question 1

Nodal Analysis Steps

Answer 1

1. Identify all nodes (three or more connections) of the circuit
2. Set one node as ground
3. Define directions of the currents at remaining nodes
4. Unknown node potentials are the voltages with respect to earth/ground
5. Write out KCL equations for all nodes but ground node
6. Use KVL and Ohm’s law to express unknown currents using unknown voltages
7. Rearrange for unknown currents, put into KCL equations and solve for the unknown voltages

Question 2

Power dissipated across resistor

Maximum power dissipated across resistor

Answer 2

P=(V^2)/R
Where V is the voltage across it

Assume resistor after voltage source = resistor we’re measuring
P=(V^2)/4R

Question 3

Equations:
Charge, voltage and capacitence
Charge and current
Energy, capacitance and voltage

Answer 3

Q=CV
Q=∫i(t) dt between T and 0
E=0.5C(V^2)

Question 4

Current and voltage across capacitor equation involving current, capacitance and voltage

Answer 4

i(t) = C * (dV(t)/dt)
V(t) = (1/C) * ∫ i(t) dt

Question 5

Current given by a discharging capacitor
Initial current
Voltage across a charging capacitor

Answer 5

i = i(0) * e^(-t/RC)
i(0) = V(0)/R
V = Vs*(1 - e^(-t/RC)

Question 6

Voltage across an inductor
Current across an inductor
Energy stored in an inductor

Answer 6

V(t) = L * (di/dt)
i(t) = 1/L * ∫ V(t) dt
E=0.5LI^2

Question 7

Parallel capacitors: voltage, charge and capacitance across them
Maximum safe operating voltage when combining capacitors

Answer 7

Voltage: V1 = V2 = V (KVL)
Charge: Q = Q1 + Q2
Capacitance: C = C1 + C2

Vmax = lowest safe maximum voltage

Question 8

Series capacitors: voltage, charge and capacitance across them

Answer 8

Voltage: V = V1 + V2 (KVL)
Charge: Q = Q1 = Q2
Capacitance: 1/C = 1/C1 + 1/C2

Question 9

Maximum safe operating voltage for capacitors in series: formula

Answer 9

IF (C1/C2)V1max < V2max
Vmax = V1max + (C1/C2)V1max

IF (C2/C1)V2max < V1max
Vmax = V2max + (C2/C1)V2max

Question 10

Key equations for:
AC sine waves voltage and current
Angular frequency
Frequency/period

Answer 10

v = V̂ * sin(ωt)
i = Î * sin(ωt) = (V̂/R)*sin(ωt)
V̂/Î  = amplitude
R = resistor
ω = 2π*f
f = 1/T

Question 11

Equations for power in an AC sine wave:
Instantaneous power
Average power

Answer 11

P = v*i = (V̂ * sin(ωt)) * (V̂/R)*sin(ωt)
Pav = (V̂ * Î)/2

Question 12

Formula for RMS of periodic waveforms

Answer 12

( (1/T)*∫ (v(t))^2 dt )^0.5
Integtrate between period T and 0
If v(t) is not a sine wave, just square the amplitude

Question 13

Capacitor vs inductor: does current lead or does voltage? Remember CIVIL
Resistor, current or voltage lead?

Answer 13

Capacitor: current leads voltage (CIV) by 90°
Inductor: voltage leads current (VIL) by 90°
Resistor: current and voltage are in phase

Question 14

Reactance and impedance of a capacitor

What does a capacitor do to DC signals?

Answer 14

Xc = -1/ωC
Impedance = Resistance + j*reactance
You may have to take the modulus of it to get a real value
It blocks them

Question 15

Reactance of an inductor

What does an inductor do to DC?

Answer 15

Xl = ωL
Impedance = Resistance + j*reactance
You may have to take the modulus of it to get a real value
It lets it pass

Question 16

Complex Ohms law equations for resistors, capacitors and inductors?
How to sub in current/voltage aka find current/voltage across these components?

Answer 16

Z = R
Z = -j/ωC
Z = jωL
Sub in Z = V/I

Question 17

Simplifying circuits using complex Ohm’s law: Z components in series vs in parallel
What do you need to remember to do with the final Z thingy?

Answer 17

In series: Z = Z1 + Z2
In parallel: 1/Z = 1/Z1 + 1/Z2

Split into real and imaginary parts

Question 18

What is the transfer function H(ω)? How to get rid of the imaginary parts for | H(ω) |?

Answer 18

Voltage ratio, Vout/Vin

Take modulus of everything-square and square root everything

Question 19

Plotting voltage and current AC sine waves as phasers

Working backwards to find phase angle between voltage and current

Answer 19

Plot on x y graph
Length of line = amplitude
Angle from x axis = ω

Angle (Ф) = arctan(| (Xl/Xc) |/R)
Xl/Xc = reactance
R = resistance

Question 20

4 types of filters and how they react to different frequencies

Answer 20

Low-pass filter: only lets low frequency signals through
High-pass filter: only lets high frequency signals through
Band-pass filter-only lets signals in a certain range of frequencies through
Band-stop/notch filter: stops frequencies in a certain range from going through

Question 21

How to tell if an impedance Z is in resonance?

Good values to sub in for ω0 and Q when dealing with H(ω)

Answer 21

If the imaginary part of Z is 0

ω0: 10^3
Q = 10^1, 10^2, 10^3, 10^4

Question 22

Formula for reactive instantaneous ‘power’ for capacitor and inductor

Answer 22

p = ((V̂ )^2) / 2*| Xc |
V̂  = amplitude of voltage sine wave
p = ((V̂ )^2) / 2*Xl

Question 23

Average reactive power formula for resistor, capacitor and inductor

Answer 23

P = V*I*cos(Ф)
Ф = phase angle between voltage and current
Examples: resistor, Ф=0, P=VI
Capacitor, Ф = 90°, P = 0
R/C combination, 0°

Question 24

Formula for power factor, apparent power and another formula for reactive power similar to those two

Answer 24

PF = Pav / (VI)
AP = VI
Reactive power = VI|sin(Ф)|

Question 25

Symbols and units for active (real) power/resistive power, reactive power, complex power, apparent power
What do you have to remember about complex power?

Answer 25

AP: P, W
RP: |Q| ,var
CP: S = P + jQ
AP: |S|, VA
S = V * I* 
I* = complex conjugate of current

Question 26

Phasers: best way to work them

Answer 26

V/I = Z

Question 27

Maximum power transfer for RLC circuits

Answer 27

Maximum power is transferred IF Zs* = ZL
Where Zs* is the complex conjugate of the first Z. This means Rs=RL and -Xs=XL

P = (|Vs|)/4*Rs
Where Rs is the real part