EE221 - Practice for the Midterm Exam

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Gladys Pearson
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1 EE1 - Practice for the Midterm Exam 1. Consider this circuit and corresponding plot of the inductor current: Determine the values of L, R 1 and R : L = H, R 1 = Ω and R = Ω. Hint: Use the plot to determine values of D, E, F and a such that the inductor current can be represented as D for t 0 i() t = at E + Fe for t 0

2 . Design the circuit in (a) to have the response in (b) by specifying the values of C, R 1 and R. C = F, R 1 = Ω and R = Ω. 3. Here are three ac circuits, each represented in the frequency domain. The input to each of these circuits is the phasor voltage V s = V. Let P a, P b and Pc denote the average power supplied by the source in circuit (a), (b) and (c) respectively. Determine the values of P a, P b and P c : P a = mw, P b = mw and P c = mw

3 4. Given that () = ( + ) vi t 4 cos 3t 75 V answer the following questions: a) Suppose R = 9 Ω and L = 5 H. What are the average, complex and reactive powers delivered by the source to the load? P = W, S = VA and Q = VAR b) Suppose the source delivers j 14.1 VA to the load. What are the values of the resistance, R, and the inductance, L? R = Ω and L = H c) Suppose the source delivers 14.1 W to the load at a power factor of lagging. What are the values of the resistance, R, and the inductance, L? R = Ω and L = H 5. Given that vi () t = 4 cos( 3t+ 75 ) V Determine the impedance of the load and the complex power delivered by the source to the load under each of the following conditions: a) The source delivers j 8.47 VA to load A and j 14.1 VA to load B. Z = Ω, S = VA b) The source delivers j 14.1 VA to load A and the impedance of load B is 15 + j 9 Ω. Z = Ω, S = VA c) The source delivers 14.1 W to load A at a power factor of lagging and the impedance of load B is 9+ j15ω. Z = Ω, S = VA d) The impedance of load A is 15 + j 9 Ω and the impedance of load B is 9+ j15ω. Z = Ω, S = VA

4 6. In this circuit an ac source is connected to a load by the line. The load voltage is V L = 10 0 Vrms and the load receives 50 W at a power factor of 0.8 lagging. The line current is I = Arms Determine the RMS value of required source voltage, v s (t), and the average power supplied by the source, P s. Vs = Vrms and P s = W 7. In this circuit an ac source is connected to a load by the line. The load voltage is V L = 10 0 Vrms and the load receives 50 W at a power factor of 0.8 lagging. The line current is I = B φ Arms Determine the values of B and φ. B = Arms and φ = 8. The input to this circuit shown is () = ( ) vs t 1cos 5 t V The impedance of the load is 0 + j 15 Ω. Noticing that i 1 (t) and i (t) are mesh currents, we can represent this circuit by the mesh equations 0 + ja jb I = jc 0 + jd 0 I where a, b, c, and d are real constants. Determine the values of a, b, c, and d. a = Ω, b = Ω, c = Ω, and d = Ω 9. This circuit consists of a source connected to a load by coupled coils. The input is () = ( ) vs t 1cos 5 t V The impedance of the load is 0 + j 15 Ω. The mesh currents i 1 (t) and i (t) are () = ( ) and i ( t) = ( t ) i1 t cos 5t.8 A cos 5.86 A Determine the values of S, the complex power supplied by the source, S c, the complex power received by the coupled inductors and S L, the complex power received by the load. S = + j VA, S c = + j VA and S L = + j VA

represent complex numbers in rectangular form. Determine the following: a =, b =, c =, d =, f = 11.

5 10. Here is a circuit containing coupled coils, represented in the frequency domain. The currents I 1 and I are mesh currents. The mesh equations representing this circuit can be expressed as ( a jb) ( c jd) + I1+ + I = ( c jd) ( j f ) + I I = 0 1 where a+ jb, c+ jd, and 40 + j f represent complex numbers in rectangular form. Determine the following: a =, b =, c =, d =, f = 11. The current i(t) and voltage v(t) labeled on the circuit drawing are ( t ) it ( ) = cos A and vt ( ) = cos 3 t+ V ( ) 1. The current i(t) and voltage v(t) labeled on the circuit drawing are ( t ) it ( ) = cos A and ( t ) vt ( ) = cos 4 V 13. Determine the values of R and L: R = Ω and L = H

6 14. This circuit consists of a load connected to a source through an ideal transformer. The input to the circuit is vs () t = 1 cos( 0 t) V Determine the values of the turns ration, n, and load inductance, L, required for maximum power transfer to the load. n = and L = H 15. This circuit consists of a load connected to a source through an ideal transformer. The input to the circuit is () = ( ) vs t 1 cos 0 t V The coil voltages and currents are () ( ) v1 t = Acos 0t V, () = ( + ) v t Bcos 0t 15.5 V () = ( ) and i ( t) = D ( t+ ) i1 t Ccos 0 t A Determine the values of A, B, C and D. cos A A = V, B = V, C = A and D = A 16. This circuit consists of a load connected to a source through an ideal transformer. The input to the circuit is () = ( ) vs t 1 cos 0 t V The coil voltages and currents are () ( ) v1 t = 6.7 cos 0t V, () = ( + ) v t 4.91cos 0t 15.5 V () = ( ) and i ( t) = ( t+ ) i1 t 0.333cos 0 t A cos A Determine the values of S p, the complex power received by the primary (left) coil of the transformer and S L, the complex power received by the load. S p = + j VA and S L = + j VA

j. The table below tabulates frequency 1+ j 0 response data for this circuit. Fill in the blanks in the table: 17. The network function of a circuit is H = 10, rad/s Gain, V/V Phase Shift, 10 89.

7 j. The table below tabulates frequency 1+ j 0 response data for this circuit. Fill in the blanks in the table: 17. The network function of a circuit is H = 10, rad/s Gain, V/V Phase Shift, The network function of a circuit is H k =. The table below tabulates frequency response 1+ j p data for this circuit., rad/s Gain, V/V Phase Shift, Determine the values of p and k: p = rad/s and k = V/V 19. The input to the circuit is the voltage of the voltage source, v () t. The output is the voltage v o (t). The network i function of this circuit is H ( ) ( ) ( 0.1) = Vo j V = i 1+ j 1+ j p 15 Determine the values of the capacitance, C, and the pole, p. C = μf and p = rad/s. 0. The network function of this circuit is: Vo j Η = = ( k ) V s 1+ j p Determine the values of k and p: k =, and p = rad/s.

8 1. The input to the circuit is the voltage of the voltage source, v ( ) network function of this circuit is i t. The output is the voltage v o (t). The H Vo = = Vi 1+ 4 j 100 Determine the values of the capacitance, C, and the VCVS gain, A. C = μf and A = V/V.. The network function of this circuit is: Vo k Η = = V i 1+ j p Determine the values of k and p: k =, and p = rad/s.

EE313 Fall 2013 Exam #1 (100 pts) Thursday, September 26, 2013 Name. 1) [6 pts] Convert the following time-domain circuit to the RMS Phasor Domain.

EE313 Fall 2013 Exam #1 (100 pts) Thursday, September 26, 2013 Name. 1) [6 pts] Convert the following time-domain circuit to the RMS Phasor Domain. Name If you have any questions ask them. Remember to include all units on your answers (V, A, etc). Clearly indicate your answers. All angles must be in the range 0 to +180 or 0 to 180 degrees. 1) [6 pts]