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
. 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 = 5. 75 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
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 8.47 + 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 0.857 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 14.1 + j 8.47 VA to load A and 8.47 + j 14.1 VA to load B. Z = Ω, S = VA b) The source delivers 8.47 + 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 0.857 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
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 = 1.04 36.87 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 1 1 0 = 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 0.4676cos 5t.8 A 0.1998cos 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
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 = 15 30 ( c jd) ( j f ) + I + 80 + 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 3 + 68.4 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 4 51.3 A and ( t ) vt ( ) = cos 4 V 13. Determine the values of R and L: R = Ω and L = H
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+ 15.5 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 0 180 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+ 15.5 V, () = ( + ) v t 4.91cos 0t 15.5 V () = ( ) and i ( t) = ( t+ ) i1 t 0.333cos 0 t A 0.0833cos 0 180 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 89.44 40 153.4 18. 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, 10 17.18 17.4 40 11.5 51.3 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.
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.