Electotechnology

Question 1

Motor Power Equations

Answer 1

Pmech = T * omega
where T = torque, omega = rotational speed

Pmech = Pelec = E * I
where E = Back EMF, I = Current

Question 2

Difference between Brushed and Brushless Motors

Answer 2

Brushed motors have a commutator ring to flip the direction of current to keep the motor turning in the right direction using a DC power supply. They introduce mechanical and electrical losses and require maintenance.

Breushless motors have a different arcitecture, meaning the permanent magnet is located on the rotor while the windings are found on the casing / stator. The change in the direction of the current is timed by a separate controller that detects the position of the rotor using a Hall-effect sensor.

Question 3

General Motor Equations

Answer 3

F = 𝐼d × B, force on each wire

T=2r × F = 2r × 𝐼d × B = k * 𝐼, torque from looped wire. So times by n, number of wires, to obtain total torque.

Question 4

Difference between High pass and Low pass filter

Answer 4

A high pass filter blocks the transmission of low frequency signals, whereas a low pass filter blocks the transmission of high frequency signals.

For low pass filters, Inductor comes before the resistor for a RL filter and the resistor comes first for a RC filter

For high pass filters, resistor comes before the inductor for a RL filter and the capacitor comes first for the RC filter

Question 5

Cut off Frequency

Answer 5

All low-pass filters are rated at a certain cutoff frequency. That is, the frequency above which the output voltage falls below 70.7% of the input voltage.

f = 1/ (2piR*C)

Question 6

Resistance of a Wire

Answer 6

R = (rho*l)/A

where rho = specific resistance, l = length, A = area

Question 7

Kirchhoff’s Voltage Law

Answer 7

The algebraic sum of voltage rises and drops along a closed circuit loop is zero.

e.g. 𝑉𝐴 − 𝑉𝐵 = 𝐼𝑅1 − 3𝑉 + 𝐼𝑅2 + 4𝑉 + 𝐼𝑅3

Question 8

Kirchhoff’s Current Law

Answer 8

The sum of the currents entering a junction must equal the sum of the currents leaving the junction.

Question 9

Time response of Inductors and Capacitors

Answer 9

Inductors :
I(t) = (V/R)(1-e^(-(R/L)t))

Capacitors :
Vc(t) = V(1-e^(-(1/RC)*t))

Question 10

Reactance

Answer 10

Reactance results as a ratio between voltage and current, it is purely imaginary.
Units are Ohms.
To compute reactance use the equation for impedance for inductors and capacitors, only difference is that there is no resistor present?

Question 11

Admittance and susceptance

Answer 11

Y_L = 1/R - j1/(Lomega)

Y_C = 1/R + jComega

where the second part of each equation (complex part) is the susceptance.

Susceptance is the inverse of reactance, It is purely imaginary.
Units are Siemens [S].

Question 12

Resonance

Answer 12

Occurs when both an inductor and capacitor are present in a circuit, can be both series or parallel.
omega = resonance freq = 1/sqrt(LC)

When a resistor is added to the circuit the current through the resistor is found by
V/R * e^(jomegat)

In series circuits the current maximises at resonance whereas in parallel circuits voltage becomes maximum.

Question 13

Magnetic fields and Magnets

Answer 13

F = q*V x B = force on moving charge
where B = magnetic field strength and V = velocity of charge

B = mu_0 * H
where mu_0 = The proportionality constant = 4𝜋 × 10−7 and H = actual magentic field strength.

In a ferromagnetic material: B = μ𝑟μ0H

H = (N*i)/l , where N = number of coils around core, i = current, l = mean length of the core.

Magnetic fluc density = AB = 𝜇𝑟𝜇0ΑH = phi

Electromotive force = N*i

Magnetic resistance = F/phi

Question 14

Analysis of frequency filters

Answer 14

RC low pass : R1 C2
𝐺 (𝑗𝜔) =(𝑈𝑜𝑢𝑡 (𝑗𝜔)) / (𝑈𝑖𝑛 (𝑗𝜔)) = (𝑍𝐶 (𝑗𝜔))/(𝑍𝐶 (𝑗𝜔) + 𝑍𝑅 (𝑗𝜔)) = 1/(1 + 𝑗𝜔𝐶R)

LR low pass : L1 R2
𝐺 (𝑗𝜔) = (𝑍R (𝑗𝜔))/(𝑍L (𝑗𝜔) + 𝑍𝑅 (𝑗𝜔)) = 𝑅/(𝑗𝜔𝐿 + R)

RC high pass : C1 R2
𝐺 (𝑗𝜔) =(𝑈𝑜𝑢𝑡 (𝑗𝜔)) / (𝑈𝑖𝑛 (𝑗𝜔)) = (𝑍𝑅 (𝑗𝜔))/(𝑍𝐶 (𝑗𝜔) + 𝑍𝑅 (𝑗𝜔)) = (𝑗𝜔𝐶𝑅)/(1 + 𝑗𝜔𝐶𝑅)

LR high pass : R1 L2
𝐺 (𝑗𝜔) = (𝑍L (𝑗𝜔))/(𝑍L (𝑗𝜔) + 𝑍𝑅 (𝑗𝜔)) = (j𝜔(L/R))/(j𝜔(L/R) +1)

Where G is the transfer function

Question 15

Sparks

Answer 15

A spark requires a certain energy to stay ionised. It becomes more conductive the more current flows, lowing the voltage.

𝐼 ≈ 𝑃/U

Question 16

What does MOSFET stand for?

Answer 16

Metal Oxid Semiconductor Field Effect Transistor

Question 17

Maximum Power Transfer Theorem

Answer 17

To generate maximum external power through a finite internal resistance (DC network), the resistance of the given load must be equal to the resistance of the available source.