Energy Storing Elements

Question 1

Complex Numbers (j)

Answer 1

• Use j for imaginary numbers
• Exponential form (Euler) is good for multiplication/division.
• Cartesian form is good for adding/subtracting.

Question 2

Exponential form (Euler) Complex Numbers

Answer 2

Ae^(jθ)
- Where A is the magnitude ( A = srt(a^2 + b^2))
- θ is the angle (θ = atan(b/a))

Question 3

Cartesian form Complex Numbers

Answer 3

a + bj

Question 4

Periodic Signals

Answer 4

Exponential representation: Ae^(j(ωt + φ))

Where
A is amplitude
ω is angular frequency (rad/s)
t is time
φ is any phase in the cycle

Question 5

Inductors

Answer 5

• Stores energy in a magnetic field when electric current flows through it. An inductor typically consists of an insulated wire wound into a coil.
• More coil means more inductance.
• When current flows through a conductor it causes a change in magnetic flux, causing a voltage to be created at the terminals of the inductor.

Question 6

Inductance Formulae

Answer 6

• A change in current over time causes a change in magnetic flux over time, causing a voltage at the terminals of the inductor.
• Voltage is proportional to the rate of increase of current.
• The Proportionality constant is L (inductance)

V = L (dI/dt) (for series)
&raquo_space;» rearrange to get I
I = (1/L) integral(Vdt) (for parallel)

Where
V is voltage
L is inductance in Henry (1Volt*1sec)/1A
I is current
t is time

Question 7

Inductance formulae Series or Parallel?

Answer 7

Series: V = L (dI/dt)
- Sum of voltage equals zero

Parallel: I = (1/L) integral(Vdt)
- Kirchhoff’s Current law, current splits.

Question 8

Energy Storage in Inductors

Answer 8

• Energy is stored in the magnetic field created when current flows through the inductor.
• When the current is cut off, this magnetic energy is passed back to the inductor to create a difference in potential at its terminals.

E = 1/2LI^2

Question 9

Inductors in Series

Answer 9

The total is the sum of individual inductances.

Question 10

Inductors in Parallel

Answer 10

1/L(TOTAL) = 1/L1 + 1/L2 + 1/L3…

Question 11

Capacitors (Structure)

Answer 11

• Consist of two thin conductive plates positioned opposite each other with a very small gap, where the gap is filled with air or any dielectric material

Question 12

Capacitors (What do they do?)

Answer 12

• Energy storing elements.
• Electrons (current) will flow toward the plate connected to the anode (-ve) and away from the plate connected to the cathode (+ve).
• The plates gradually become electrically charged and this charge results in a voltage developing at the terminal of the capacitor.
• The voltage becomes equal to that of the source and current stops completely, the capacitor is then fully charge.
• The voltage lags the current!

Question 13

Capacitor Equations

Answer 13

• When capacitor fully charged, it has stored charge (q).
• Ratio of charge over voltage, or charge per unit voltage.

C = q/V
Unit of Farad

Question 14

Capacitor in terms of Voltage and Current (formula sheet)

Answer 14

Series: V = q/C&raquo_space;> 1/C (integral(I dt))

Parallel: q = CV&raquo_space;> dq/dt = I = C(dV/dt)

Question 15

Energy Storage in Capacitors

Answer 15

• Energy is stored in an electrostatic field.
• Voltage (V) is related to change in energy (dE) per charge (dq)

V = dE/dq
&raquo_space;>
E = 1/2 CV^2

Question 16

Physical Interpretation of Inductor/Capacitor circuits

Answer 16

• The response is always exponential, which means it gradually develops until some saturation level is achieved.
• Where it has either:
  > Stored all the available energy
  > Released all of the stored energy into the circuit ending up with zero charge

Question 17

Capacitors in Series

Answer 17

1/C(TOTAL) = 1/C1 + 1/C2 + 1/C3…

Question 18

Capacitors in Parallel

Answer 18

C(TOTAL) = C1 + C2 +C3…