EE301 Final Exam:�Review

Jeopardy!

6 Weeks $100

An indicator lamp on a control panel operates continuously, drawing 20 mA from a 120V supply. At $0.09 per kWh, how much does it cost per year to operate this lamp?

12 Weeks $100

Using source transformations, determine the voltage drop VR across the 10 ohm resistor.

X-formers $100

For the figure below i₁ = 100 sin (ωt) mA and the transformer is ideal.

Determine the secondary currents i₂ and i₃.

Note the dot convention here, which switches the polarity 180⁰

Linear and DC Motors $100

A 100V linear motor operates with a magnetic field of 0.5 Tesla, and a mechanical loading of 1.0N. The effective length of the bar is 0.1m, and the rail resistance is 0.02 Ω.

Find the current flowing through the motor and the velocity of the bar when steady-state conditions are achieved.

Current at steady-state:

To find velocity (u):

E_AB = 208∠0° V .

Find the phase voltages and line currents.

3-Phase Power $100

Phase Voltages:

Line Voltages:

Phase/Line Currents:

-

+

AC Generator $100

a) For a 4 pole, 60 HZ generator, what is the speed in rpm of the rotor? b) What would be the frequency of a 6 pole machine spinning at the same rpm?

Given the circuit below:

1. Determine I_T
2. Detemrine I₁
3. Deteremine V_a
4. Determine V_ad
5. Determine P_T

​

6 Weeks $200

R_T = {[(150Ω+50Ω)ll300Ω+80Ω]ll200Ω}+25Ω+75Ω = 200Ω

​

1. I_T = E_T/R_T = 28V/200Ω = 140mA
2. I₁ = I_Tx(R_eq /R₂₀₀) = 140mA x 100 Ω/200Ω = 70mA
3. V_a = I_TxR₇₅ + I₁xR₂₀₀ = (140mA)(75 Ω) + (70mA)(200 Ω) = 24.5V
4. V_ad = I₁xR₂₀₀ = (70mA)(200 Ω) = 14V
5. P_T = E_TxI_T = 28V x 140mA = 3.92W

​

Determine the nodal equations and voltages at node a and b.

​

12 Weeks $200

X-formers $200

An amplifier is modeled with a Thèvenin equivalent impedance of 36-54j Ω.

1. What load impedance must be chosen to ensure maximum power transfer occurs?
2. What is the transformer load apparent power (VA) for this value of Z_LD?

Now find the xfmr load impedance:

Linear and DC Motors $200

Design a 10 kW (output power) Linear Motor that reaches 100 km/hr. Maximum B-field is 3 T. We have a 450 V DC source available. The system desired efficiency is 95%.

Find the required rail resistance, source current, and bar length.

3-Phase Power $200

E_AN=120∠-30 V.

a) Determine per phase and total power (active, reactive, and apparent).

system is inductive (+VAR)

AC Generator $200

Consider a 3-phase, 4 pole, 60Hz, 450V synchronous generator rated to supply 1687.5 kVA to a ship distribution system requiring a 0.8 lagging power factor.

1. If this machine was operating at rated conditions, what is the real (P) power, reactive (Q) power and the current (I) being supplied to the load?
2. When efficiency (η) is 95%, what torque does the prime mover provide?
3. What is the speed of the rotor (N) in rpm?

6 Weeks $300

Using Nodal Analysis, solve for I_UNK

12 Weeks $300

Determine Z_LD that will allow maximum power to be delivered to the load in the circuit below. Then find the power dissipated by the load.

X-formers $300

Use the reflected impedance concept to solve for the total impedance Z_T as seen by the Source. Determine I_g and I_LD.

​

Linear and DC Motors $300

We wish to design a 1/4 hp, 28 V DC motor with an efficiency of 96%.

1. What current can we expect to draw?
2. If the machine constant is K_v= 0.2139 ν·s, determine T_out if we ignore mechanical losses.
3. Calculate rated speed in rpm.

​

​

0

3-Phase Power $300

E_AB = 208∠0° V. Determine:

a. Determine the line currents

b. Determine total real power delivered by the

generator

c. Total real power dissipated by the load

d. Determine the load phase voltage Van

AC Generator $300

6 Weeks $400

a

b

6 Ω

3 Ω

2 F

3V

60V

The switch has been in position a for a long time. At time t=0, it moves to position b.

1. Calculate the steady state voltage across the capacitor at position a
2. Calculate the steady state voltage across the capacitor at position b
3. Calculate the time constant (tau) in position b
4. Find the voltage v(t) across the capacitor for t>0
5. Find the energy stored by the capacitor at t=60 secs

​

1. V_c at SS = V across R₂. Use VDR understanding Capacitor is an open circuit. (Think Thevenin)

V_c at SS = E x R₂/R_T

R_T = 6 Ω + 3 Ω = 9 Ω

V_c = 3V x (3 Ω / 9 Ω) = 1V

b. Similar to a.

V_c = 60V x (3 Ω / 9 Ω) = 20V

3. Tau = RC. Think Thevenin for R

R = 6Ωll3Ω = 2Ω

Tau = 2Ω x 2F = 4sec

4. V_c(t) = V_f + (V_i – V_f)e^-t/tau

V_c(t) = 20+(1-20)e^-t/4sec = 20-19e^-t/4V

5. E = ½ CV²

E = ½ (2F)(20V)² = 400J

12 Weeks $400

Determine f_r, Q, BW and the current (I) at resonance. Plot the current vs. frequency and label f_r, f₁, f₂ and BW.

1Ω

X-formers $400

​

DAILY DOUBLE

Linear and DC Motors $400

Consider a 0.25 hp, 28 V DC motor rated for 3500 RPM and has an efficiency of 96%.

1. Find I_a.
2. Determine R_a.
3. Find the Machine Constant (K_v).
4. Determine T_load with no mechanical losses.

3-Phase Power $400

E_AB=480∠0 V. Frequency 60 Hz.

Determine value of capacitor which must be placed across each phase of the motor to correct to a unity power factor.

The Q_φ is what will be used for Q_c in determining the value of the capacitor to used

AC Generator $400

An Arleigh-Burke Class destroyer has a 3-phase, Y-connected, 4-pole, 60 Hz synchronous generator, rated to deliver 3.75 MVA with a 0.8 lagging power factor and a line voltage of 450 V. The machine stator resistance is negligible and the synchronous reactance is equal to 0.04Ω. The actual system load on the machine draws 2 MW at a 0.8 Fp lagging. Assume that a voltage regulator has automatically adjusted the field current so that the terminal voltage, VAN, is at its rated value.

a. What is the rated speed?

b. Determine the reactive and apparent power delivered by the generator.

c. Find the current drawn from the generator using the terminal voltage, VAN , as the reference phasor.

d. Determine the induced voltage, Einduced

X-formers $400

An amplifier is modeled with a Thèvenin equivalent impedance of 320-160j Ω. A transformer is used to impedance match the load to the source to ensure max power transfer.

1. What turns ratio should be chosen for the transformer, and what value of load resistance should be chosen to ensure max power transfer?
2. What is the real and reactive power of the load? What is the real and reactive power delivered by the source?

NOTE: we only need to look at the reactance for max power to the turns ratio (a).

Now we know (a) we can find the real (R) resistive portion:

80Ω

2

X-formers $400

An amplifier is modeled with a Thèvenin equivalent impedance of 320-160j Ω. A transformer is used to impedance match the load to the source to ensure max power transfer.

1. What turns ratio should be chosen for the transformer, and what value of load resistance should be chosen to ensure max power transfer?
2. What is the real and reactive power of the load? What is the real and reactive power delivered by the source?

Remember that X_pri = X_LD are matched therefore cancel each other out (-j160=j160)

=>This implies xfmr Pin = 7.8W, which = Pout of 7.8W