EE301 Final Exam Review

Final Exam Review

1) Determine the total resistance (𝑽𝑽𝑶𝑶) seen by the source and the currents (𝑰𝑰𝒔𝒔), (𝑰𝑰𝟏𝟏), and (𝑰𝑰𝟐𝟐) in theDC circuit below.

2) Find the power delivered by the source (𝑷𝑷𝒔𝒔) and the power absorbed by all of the resistors(𝑷𝑷𝟏𝟏𝟑𝟑), (𝑷𝑷𝟏𝟏𝟐𝟐), (𝑷𝑷𝟏𝟏𝟐𝟐), and (𝑷𝑷𝟐𝟐). Does the power being delivered equal to the total power beingabsorbed?

3) Use nodal analysis to find the voltage at the node (𝑽𝑽). Now use Ohm’s Law to find the voltageacross the 12 Ω resistor. Do these voltages equal each other?

𝑰𝑰𝒔𝒔 +-

10 Ω

𝟑𝟑𝟑𝟑 𝑽𝑽 𝑰𝑰𝟏𝟏 𝑰𝑰𝟐𝟐

15 Ω

5 Ω 12 Ω

𝑉𝑉

4) Determine the total impedance (𝒁𝒁𝑶𝑶) seen by the source and the currents (𝑰𝑰𝒔𝒔), (𝑰𝑰𝟏𝟏), and (𝑰𝑰𝟐𝟐) inthe AC circuit below.

5) Find the complex power delivered by the source (𝑺𝑺𝑶𝑶 ) and the Real/Reactive power of theelements (𝑷𝑷𝒋𝒋), (𝑷𝑷𝟏𝟏𝟐𝟐), (𝑸−𝒋𝒋𝟏𝟏𝟑𝟑), (𝑷𝑷𝟏𝟏𝟒𝟒), (𝑷𝑷𝟏𝟏) and (𝑸𝒋𝒋𝟏𝟏𝒋𝒋). Does the source complex power equal tothe total Real and Reactive power of the elements?

𝑰𝑰𝒔𝒔

8 Ω

𝑰𝑰𝟏𝟏 𝑰𝑰𝟐𝟐

14 Ω

6 Ω 12 Ω

+ -

𝟐𝟐𝟐𝟐∡𝟏𝟏𝟐𝟐𝒐𝒐 𝑽𝑽 j18 Ω

-j10 Ω

6) What is the difference between Apparent Power and Complex Power?

7) Find the power factor (𝝁𝝁𝒑𝒑) for the given Complex Power. Make sure to include if it is Leading orLagging.

a. 𝑆 = 322∡30.25𝑜 𝑉𝑉𝐴

b. 𝑆 = 259− 𝑗324 𝑉𝑉𝐴

8) An AC circuit operates at a frequency of 𝟏𝟏.𝟒𝟒𝟏𝟏𝟐𝟐 𝒌𝑯𝒛 and its impedance is 𝒁𝒁 = 𝟗𝟐𝟐 + 𝒋𝒋𝟏𝟏𝟑𝟑𝟑𝟑 Ω. Isthe impedance Inductive or Capacitive? What is the Inductive/Capacitive component value?

9) An AC circuit operates at a frequency of 𝟑𝟑𝒋𝒋𝟑𝟑.𝟏𝟏𝟒𝟒 𝒓𝑳𝑳𝑳𝑳/𝒔𝒔 and its impedance is 𝒁𝒁 = 𝟑𝟑𝟐𝟐 − 𝒋𝒋𝟏𝟏𝟒𝟒𝟐𝟐 Ω.Is the impedance Inductive or Capacitive? What is the Inductive/Capacitive component value?

10) The following circuit is operating at a frequency of 𝝎 = 𝟐𝟐𝟑𝟑𝟑𝟑 𝒓𝑳𝑳𝑳𝑳/𝒔𝒔.

a. Draw the Power Triangle for the Load and label the Apparent, Real, and Reactive Power. Also include the Complex Power angle.

b. Find the source current (𝑰𝑰𝒔𝒔).

c. Typically we like to reduce the source current. This can be accomplished by connecting a Capacitor in parallel to an Inductive Load. The Capacitor component value (𝑪𝑪) is determined by choosing a Capacitance Reactive Power (𝑸𝒄𝒄) equal to the Inductance Reactive Power (𝑸𝑳𝑳). Find the Capacitor component value so all of the Reactive Power at the Load is cancelled. In other words, what component value will correct the power factor to unity?

𝟏𝟏𝟏𝟏𝟑𝟑 𝑾𝑾

+

-

𝟐𝟐𝟐𝟐𝟑𝟑∡𝟒𝟒𝟑𝟑𝒐𝒐 𝑽𝑽

𝑰𝑰𝒔𝒔

𝟒𝟒𝟑𝟑𝟑𝟑 𝑽𝑽𝑽𝑽𝑽𝑽

d. Find the source current (𝑰𝑰𝒔𝒔) when a Capacitor is connected in parallel with the Load. Assume the Capacitance Reactive Power is −𝟒𝟒𝟑𝟑𝟑𝟑 𝑽𝑽𝑽𝑽𝑽𝑽.

11) Find the Primary (𝑰𝑰𝒑𝒑) and Secondary (𝑰𝑰𝒔𝒔) currents for the circuit shown below.

𝟏𝟏𝟏𝟏𝟑𝟑 𝑾𝑾

+

-

𝟐𝟐𝟐𝟐𝟑𝟑∡𝟒𝟒𝟑𝟑𝒐𝒐 𝑽𝑽

𝑰𝑰𝒔𝒔

𝟒𝟒𝟑𝟑𝟑𝟑 𝑽𝑽𝑽𝑽𝑽𝑽

−𝟒𝟒𝟑𝟑𝟑𝟑 𝑽𝑽𝑽𝑽𝑽𝑽

𝑰𝑰𝟏𝟏 𝑰𝑰𝟐𝟐

𝟏𝟏𝟑𝟑∡𝟑𝟑𝒐𝒐 𝑽𝑽

𝑰𝑰𝒑𝒑

+ -

𝟏𝟏𝟑𝟑 Ω 𝒋𝒋𝟏𝟏𝟐𝟐 Ω

−𝒋𝒋𝒋𝒋 Ω

𝟏𝟏Ω

𝑰𝑰𝒔𝒔

4 : 6

12) Refer to the circuit in problem 11. What component values do we need if we treat the secondary side as the Load and can replace the Load impedances (𝒁𝒁𝑳𝑳𝒐𝒐𝑳𝑳𝑳𝑳) with components that will achieve Maximum Power Transfer?

13) Find the Thevenin Equivalent (𝑽𝑽𝑶𝑶𝑯) and (𝒁𝒁𝑶𝑶𝑯) for the circuit below.

a. Determine the Load (𝒁𝒁𝑳𝑳𝒐𝒐𝑳𝑳𝑳𝑳) that will achieve Maximum Power Transfer and draw the Thevenin Circuit with the Load.

𝟐𝟐∡𝟒𝟒𝟏𝟏𝒐𝒐 𝑽𝑽

100 Ω 220 Ω

𝒁𝒁𝑳𝑳𝒐𝒐𝑳𝑳𝑳𝑳

j30 Ω

-j50 Ω

-j20 Ω

14) Find the time constants for the circuit below if:

a. The switch is in the (𝒏𝒏) position for a long time and then moves to position (𝟏𝟏) until steady-state is reached. Is the Capacitor Charging or Discharging?

b. The switch is in the (1) position for a long time and then moves to position (2) until steady-state is reached. Is the Capacitor Charging or Discharging?

15) In the Linear Motor below (𝑽𝑽𝒔𝒔 = 5.5 𝑘𝑉𝑉), (𝜷 = 8𝑇), (𝑽𝑽𝑽𝑽 = 12 Ω), and (𝑳𝑳 = 3𝑚). At (𝑡 = 0) the switch is closed. Assume the sliding bar is initially at rest and there is no mechanical friction.

a. Find the initial current and Force just after the switch is closed.

120 V 30 Ω

1 2 𝑪𝑪 = 𝟑𝟑𝟑𝟑𝟑𝟑.𝟑𝟑𝟑𝟑𝝁𝝁𝝁𝝁

+ -

50 Ω

+

- 𝑽𝑽𝒄𝒄

𝒏𝒏

1 kΩ 20 Ω

12 Ω

+ -

𝑽𝑽𝒔𝒔

𝑽𝑽𝑽𝑽

𝑬𝑬𝒊𝒊𝒏𝒏𝑳𝑳

+

-

𝑳𝑳

𝑰𝑰𝒔𝒔

b. Find the velocity of the bar and Force when (𝑰𝑰𝒔𝒔 = 50 𝐴).

c. When the bar begins to move why does the current decrease?

16) Match the following definitions.

A. Converts Electrical Energy into Mechanical Energy.

B. Converts Mechanical Energy into Electrical Energy.

C. Magnetic field created by a current carrying wire interacts with an existing magnetic field to exert a developed force on the wire.

D. Movement of a conductor in a magnetic field that will induce a voltage.

E. A segmented device commonly found in DC motors that are used with brushes to reverse the direction of the applied current on the rotor.

F. A device commonly found in AC generators that are used with brushes to pass a DC current to create an electromagnet on the rotor.

G. A heavy gauge conductor that connects multiple circuits or loads to a common voltage supply.

H. The main reason an ungrounded system is used on Navy Ships.

I. A critical downside of using an ungrounded system on Navy Ships.

J. A device designed to trip when overcurrent or high currents are reached.

___ Personnel Safety

___ Faraday’s Law

___ Bus

___ Commutator

___ Equipment Reliability

___ Motor

___ Circuit Breakers

___ Slip Ring

___ Lorentz Force Law

___ Generator

17) A DC Motor was tested under two operating speeds. Find the armature resistance (𝑽𝑽𝑳𝑳), motor constant (𝑲𝒅𝒅), and the Mechanical Torque Loss (𝑶𝑶𝑳𝑳𝒐𝒐𝒔𝒔𝒔𝒔) assuming it is independent of speed. Test 1: Applied (𝒋𝒋𝟑𝟑 𝑽𝑽𝑫𝑫𝑪𝑪) and measured (𝑰𝑰𝑳𝑳 = 𝟑𝟑.𝟐𝟐 𝑽𝑽) at (𝟏𝟏𝟗𝟏𝟏𝟑𝟑 𝒓𝒑𝒑𝒎) with no load Test 2: Applied (𝒋𝒋𝟑𝟑 𝑽𝑽𝑫𝑫𝑪𝑪) and measured (𝑰𝑰𝑳𝑳 = 𝟏𝟏𝒋𝒋 𝑽𝑽) at (𝟏𝟏𝟑𝟑𝟐𝟐𝟑𝟑 𝒓𝒑𝒑𝒎) with a load

+ -

𝑽𝑽𝑫𝑫𝑪𝑪

𝑽𝑽𝑳𝑳

𝑰𝑰𝑳𝑳

+ -

𝑬𝑬𝑳𝑳

𝑷𝑷𝑰𝑰𝑰𝑰 𝑷𝑷𝑶𝑶𝑶𝑶𝑶𝑶

𝑷𝑷𝑬𝑬𝑬𝑬𝑬𝑬𝒄𝒄 𝑳𝑳𝒐𝒐𝒔𝒔𝒔𝒔 𝑷𝑷𝑴𝑴𝑬𝑬𝒄𝒄𝑴𝑴 𝑳𝑳𝒐𝒐𝒔𝒔𝒔𝒔

𝑷𝑷𝑳𝑳𝑬𝑬𝒅𝒅

a. Find (𝑷𝑷𝑰𝑰𝑰𝑰), (𝑷𝑷𝑬𝑬𝑬𝑬𝑬𝑬𝒄𝒄 𝑳𝑳𝒐𝒐𝒔𝒔𝒔𝒔), (𝑷𝑷𝑳𝑳𝑬𝑬𝒅𝒅), (𝑷𝑷𝑴𝑴𝑬𝑬𝒄𝒄𝑴𝑴 𝑳𝑳𝒐𝒐𝒔𝒔𝒔𝒔), (𝑷𝑷𝑶𝑶𝑶𝑶𝑶𝑶), and the efficiency (ƞ) of the Motor using the results from Test 2. Remember we are assuming 𝑇𝐿𝑜𝑠𝑠 is independent of speed.

18) In the balanced 3-phase circuit find the Phase Voltage (𝑬𝑬𝑽𝑽𝑰𝑰), the Line Current (𝑰𝑰𝒃𝒃), and the Total Complex Power at the Load (𝑺𝑺𝑶𝑶). Assume positive sequence and 𝑬𝑬𝑽𝑽𝑩𝑩 = 𝟑𝟑𝟒𝟒𝟏𝟏.𝟒𝟒𝟏𝟏∡𝟑𝟑𝟑𝟑𝒐𝒐 𝑽𝑽.

𝟏𝟏𝟑𝟑 Ω

𝒋𝒋𝟏𝟏𝟐𝟐 Ω

𝒋𝒋𝟏𝟏𝟐𝟐 Ω 𝒋𝒋𝟏𝟏𝟐𝟐 Ω

𝟏𝟏𝟑𝟑 Ω 𝟏𝟏𝟑𝟑 Ω

𝟏𝟏𝟒𝟒 Ω −𝒋𝒋𝒋𝒋 Ω

𝟏𝟏𝟒𝟒 Ω −𝒋𝒋𝒋𝒋 Ω

𝟏𝟏𝟒𝟒 Ω −𝒋𝒋𝒋𝒋 Ω

𝑽𝑽

𝑩𝑩 𝑪𝑪

𝑳𝑳

𝒃𝒃 𝒄𝒄

𝑰𝑰𝑳𝑳

𝑰𝑰𝒃𝒃 𝑰𝑰𝒄𝒄

𝑬𝑬𝑽𝑽𝑰𝑰 +

-

19) In the balanced 3-phase circuit find the Phase Impedance (𝒁𝒁∆) and the Phase Current (𝑰𝑰𝑳𝑳𝒃𝒃). Alsofind the Total Real (𝑷𝑷𝑶𝑶), Total Reactive (𝑸𝑶𝑶), and Total Apparent 𝑺𝑺𝑶𝑶 Power delivered by the

Generator. The per-phase Complex Power at the Load is (𝑺𝑺∅ = 𝟒𝟒𝒋𝒋𝟑𝟑 − 𝒋𝒋𝟑𝟑𝟏𝟏𝟑𝟑 𝑽𝑽𝑽𝑽),and (𝑰𝑰𝒄𝒄 = 𝟏𝟏𝟐𝟐∡𝟏𝟏𝟑𝟑𝟑𝟑𝒐𝒐 𝑽𝑽). Assume positive sequence.

𝒋𝒋𝟐𝟐𝟐𝟐 Ω 𝟐𝟐 Ω 𝑽𝑽

𝑩𝑩 𝑪𝑪

𝑳𝑳

𝒃𝒃 𝒄𝒄

𝑰𝑰𝑳𝑳

𝑰𝑰𝒃𝒃 𝑰𝑰𝒄𝒄

𝑬𝑬𝑽𝑽𝑰𝑰 +

-

𝒁𝒁∆

𝒋𝒋𝟐𝟐𝟐𝟐 Ω 𝟐𝟐 Ω

𝒋𝒋𝟐𝟐𝟐𝟐 Ω 𝟐𝟐 Ω

In previous 3-phase problems we have been only interested in the Line or Phase variables that the Generator (source) has produced to solve for the 3-phase system characteristics. In AC Generator problems we will step back to a more detail look of the internal parameters of the Generator. Remember a Generator converts Mechanical Energy from a prime mover (an axle) into Electrical Energy. An axle will rotate with an established constant magnetic field on the rotor that will induce a voltage (𝑬𝑬𝒊𝒊𝒏𝒏𝑳𝑳) on the stator windings. Before the voltage potential reaches the outer terminals of the Generator (Line Voltages) the induced voltage will suffer internal losses due to resistance of the stator windings (𝑽𝑽𝑺𝑺) and mutual inductance of the stator winding (𝑿𝑿𝑺𝑺). The circuit diagram on the left is the Single Phase Circuit of the Generator.

20) A 3-phase, Y-connected, 8-pole, 2.88 KV, 50 Hz synchronous generator is rated to deliver 4.5 MVA at a power factor of 0.883 Lagging. The per-phase stator resistance is 0.09Ω and the synchronous reactance is negligible. The AC Generator is operating at the rated Load with Mechanical Losses at 410 kW.

a. At what speed does the shaft rotate (𝒓𝒑𝒑𝒎)?

𝑽𝑽

𝑩𝑩 𝑪𝑪

𝑰𝑰𝑳𝑳

𝑰𝑰𝒃𝒃 𝑰𝑰𝒄𝒄

𝑬𝑬𝑽𝑽𝑰𝑰 +

-

𝑰𝑰 Load

𝑽𝑽 𝑰𝑰𝑳𝑳

𝑬𝑬𝒊𝒊𝒏𝒏𝑳𝑳

𝑰𝑰

𝑬𝑬𝑽𝑽𝑰𝑰

+

-

+ -

𝑽𝑽𝑺𝑺 𝑿𝑿𝑺𝑺

𝑷𝑷𝑰𝑰𝑰𝑰 𝑷𝑷𝑶𝑶𝑶𝑶𝑶𝑶

𝑷𝑷𝑴𝑴𝑬𝑬𝒄𝒄𝑴𝑴 𝑳𝑳𝒐𝒐𝒔𝒔𝒔𝒔 𝑷𝑷𝑬𝑬𝑬𝑬𝑬𝑬𝒄𝒄 𝑳𝑳𝒐𝒐𝒔𝒔𝒔𝒔

b. Find the Line Current (𝑰𝑰𝑳𝑳).

c. Find (𝑷𝑷𝑶𝑶𝑶𝑶𝑶𝑶), (𝑷𝑷𝑬𝑬𝑬𝑬𝑬𝑬𝒄𝒄 𝑳𝑳𝒐𝒐𝒔𝒔𝒔𝒔), and (𝑷𝑷𝑰𝑰𝑰𝑰) of the Generator.

d. What is the efficiency (ƞ) of the generator?

e. What is the prime mover torque?