26. For inductor voltage _____ current by ____ degrees. For capacitor voltage _____ current by ____ degrees.

1. lags,…90,…, leads, …, 90 B. leads,…90,…, lags, …, 90

C. leads,…180,…, lags, …, 90 D. leads,…90,…, lags, …, 180

E. lags,…90,…, leads, …, 180

Solution:

For inductor voltage leads current by 90 degrees. For capacitor voltage lags current by 90 degrees.

Answer: B.

27. For series RLC circuit when (R_TC)²-4LC>0 we have got _______ for solution, when (R_TC)²-4LC<0 -______, but when (R_TC)²-4LC=0-_____.

A. two complex conjugate roots, two real, unequal roots, two real, equal roots

B. two real, unequal roots, two real, equal roots, two complex conjugate roots

C. two real, unequal roots, two complex conjugate roots, two real, equal roots

D. two complex conjugate roots, two real, equal roots, two real, unequal roots

E. two real, equal roots, two complex conjugate roots, two real, unequal roots

Solution:

The characteristic equation is

LCs²+R_TCs+1=0

All possible cases of solution are:

1) (R_TC)² – 4LC > 0; 2 real unequal roots, overdamped;

v_C(t)=K₁e^-α1t+K₂e^-α2t

2) (R_TC)² – 4LC = 0; 2 real equal roots, critically damped;

v_C(t)=K₁e^-αt+K₂te^-αt

3) (R_TC)² – 4LC < 0; 2 complex conjugate roots, underdamped;

v_C(t)=K₁e^-αtcosβt+K₂e^-αtsinβt

For series RLC circuit when (R_TC)²-4LC>0 we have got two real, unequal roots for solution, when (R_TC)²-4LC<0 - two complex conjugate roots, but when (R_TC)²-4LC=0- two real, equal roots.

Answer: C.

28. For parallel RLC circuit when (G_NL)²-4LC>0 we have got _______ for solution, when (G_NL)²-4LC<0 -______, but when (G_NL)²-4LC=0-_____.

A. two complex conjugate roots, two real, unequal roots, two real, equal roots

B. two real, unequal roots, two real, equal roots, two complex conjugate roots

C. two real, unequal roots, two complex conjugate roots, two real, equal roots

D. two complex conjugate roots, two real, equal roots, two real, unequal roots

E. two real, equal roots, two complex conjugate roots, two real, unequal roots

Solution:

See Solution 78.

For parallel RLC circuit when (G_NL)²-4LC>0 we have got two real, unequal roots for solution, when (G_NL)²-4LC<0 - two complex conjugate roots, but when (G_NL)²-4LC=0- two real, equal roots.

Answer: C.

29. For capacitor the i-v-relationship is:

A.i_C(t)=(dv_C(t)/dt) B. i_C(t)= C (dv_C(t)/dt) C. v_C(t) =C(di_C(t)/dt)

D. v_C(t) =(di_C(t)/dt) E. . v_C(t) =RC(di_C(t)/dt)

Answer: B.

30. For parallel RLC circuit for solution of differential equation the characteristic equation is:

A. RCs²+G_NL+1=0 B. LCs²+G_NLs+1=0 C. LRCs²+G_NLs+1=0

D. LCs²+G_NL+1=0 E. LCs²+G_NL+1=0

Solution:

The characteristic equation is

LCs²+G_NLs+1=0

Answer: B.

31. Investigate the statements:

I. Node voltage is defined as the voltage between the definite node and the selected reference node.

II. To formulate mesh-current equations we must use branches’ conductances.

III. To apply superposition principle we must define the contribution from each source acting alone.

A. true, false, false B. false, true, false C. false, false, true

D. true, true, false E. true, false, true

Solution:

I. True.

II. False. To formulate mesh-current equations we must use branches’ resistances.

III. False, because the phrase must be continued.

To apply superposition principle we must define the contribution of each source, acting alone, and then take the algebraic sum of the components obtained.

Answer:A.

32. Ideal voltage source is described as v=____ and i=____, but ideal current source – i=_____, v=_____.

A. v_S, any value, i_S, any value B. any value, i_S, any value, v_S

C. v_S, i_S, any value, any value D. any value, any value, i_S, v_S

E. all answers are wrong

Solution:

Ideal voltage source is described as v= v_S and i= any value, but ideal current source – i= i_S, v= any value.

Answer: A.

33. In circuit analysis the homogeneity property is called _________, while the additivity property is called_______. Thevenin and Norton equivalent sources are ______ sources.

A. superposition,…. proportionality,… practical

B. superposition,…. proportionality,… ideal

C. proportionality,…superposition,…. practical

D. proportionality,…superposition,…. ideal

E. linearity, … superposition,…. ideal

Solution:

Proportionality: f(kx)=kf(x)

Superposition: f(x₁+x₂+…+x_n) =f(x₁)+f(x₂)+…+f(x_n)

In circuit analysis the homogeneity property is called proportionality, while the additivity property is called superposition. Thevenin and Norton equivalent sources are practical sources.

Answer: C.

34. If the source circuit in a two-terminal interface is linear, then the interface signals v and i do not change when the ……………. circuit is replaced by its ………………equivalent circuit.

A. interface; Thevenin or Norton B. source; Thevenin and Norton

C. interface; Thevenin D. source; Thevenin or Norton E. interface; Thevenin and Norton

Solution:

If the source circuit in a two-terminal interface is linear, then the interface signals v and i do not change when the source circuit is replaced by its Thevenin or Norton equivalent circuit.

Answer: D.

35. If the zero-input response of parallel RLC circuit is of critically damped form it has got such view:

A. i_L(t)=K₁e^-αtcosβt+K₂e^-αtsinβt B. i_L(t)=K₁e^-αtcosβt+K₂te^-αtsinβt .

C. i_L(t)=K₁e^-α1t+K₂e^-α2t D. i_L(t)=K₁e^-α1t+K₂te^-α2t

E. i_L(t)=K₁e^-αt+K₂te^-αt

Solution: see Solution 78. Answer: E.

36. Investigate the statements.

I. A phasor is a complex number representing the amplitude and phase angle of a sinusoidal voltage or current.

II. Impedance is the proportionality constant relating phasor voltage and phasor current in linear, two-terminal elements.

III. The sum of phasor currents at a node is zero

A.false, true, true B. true, false, true C. true, true, false D. true, false, false

E. false, false, true

Solution:

I. True.

II. True.

III. False. The algebraic sum of phasor currents at a node is zero.

Answer: C.

37. Impedance of capacitor is

A. Z_C= - 1/j2πfC B. Z_C= - j2πfC C. Z_C=j/2πfC D.Z_C= - j/2πfC E. Z_C=j2πfC

Solution:

Z_C = - j/ωC;

ω=2πf;

Z_C = - j/2πfC

Answer: D.

38(78). If the zero-input response of parallel RLC circuit is of overdamped form it has got such view:

A. i_L(t)=K₁e^-αtcosβt+K₂e^-αtsinβt B. i_L(t)=K₁e^-αtcosβt+K₂te^-αtsinβt .

C. i_L(t)=K₁e^-α1t+K₂e^-α2t D. i_L(t)=K₁e^-α1t+K₂te^-α2t

E. i_L(t)=K₁e^-αt+K₂te^-αt

Solution:

Zero-input response of parallel RLC circuit equation is

The characteristic equation is

LCs²+G_NLs+1=0

All possible cases of solution are:

1) (G_NL)² – 4LC > 0; 2 real unequal roots, overdamped;

i_L(t)=K₁e^-α1t+K₂e^-α2t

2) (G_NL)² – 4LC = 0; 2 real equal roots, critically damped;

i_L(t)=K₁e^-αt+K₂te^-αt

3) (G_NL)² – 4LC < 0; 2 complex conjugate roots, underdamped;

i_L(t)=K₁e^-αtcosβt+K₂e^-αtsinβt

Answer: C.

39. Investigate the statements.

1. Impedance is a phasor.

2. Susceptance is a real part of conductance.

3. For capacitor the voltage phasor lags the current phasor by 90°.

A. true, false, false B. false, false, true C. false, true, false

D. false, true, true E. true, false, true

Solution:

I. False. Impedance is the proportionality factor relating the transform of the voltage across a two-terminal element to the transform of the current through the element with all initial conditions set to zero. Phasor is a complex number representing a sinusoidal waveform.

II. False. Z = R ± jX; Y = G ± jB. Susceptance is an imaginary part of admittance. Conductance is a real part of admittance.

III. True.

Answer: B.

40. KCL states that

A. The sum of currents at a node is 0. B. the sum of currents in a loop is 0.

C. The algebraic sum of currents at a node is 0.

D. The algebraic sum of currents in a loop is 0.

E. The algebraic sum of currents at a node is 0 at every instant.

41. KVL states that

A. The sum of all voltages is 0. B. The sum of all voltages around the loop is 0.

C. The algebraic sum of all voltages around the loop is 0.

D. The algebraic sum of currents in a loop is 0.

E. The algebraic sum of all voltages around the loop is 0 at every instant.

Solution:

Kirchhoff’s voltage law (KVL) is based on the principle of conservation of energy and states that the algebraic sum of voltages around the loop is 0 at every instant.

Answer: E.

42. L=12 mH, ω=10⁶rad/s. Impedance is equal to

A. 12kΩ B.j12kΩ C. - j12kΩ D. j1200Ω E. - j1200Ω

Solution:

Z_L=jωL=j12000=j12kΩ

Answer: B.

43. Micro- means multiplication by

A. 10⁶ B. 10^-6 C. 10³ D. 10^-9 E. 10^-12

Answer: B.

44. Maximum power transfer can be calculated according to the formula

A. Pmax=V_T²/4 B. Pmax=i_N²R_T/4 C. Pmax=V_T²/2R_T

D. Pmax=V_T/4R_T E. Pmax=V_OC²/2R_T

Solution:

Answer: B.

Solution:

Kirchhoff’s current law (KCL) is based on the principle of conservation of charge and states that the algebraic sum of currents at a node is 0 for every instant.

Answer: E.

45. Ohm’s law is

A. v=Ri B. i=Gv C. v=Ri or i=Gv D. v=iG E. R=vi

Solution:

V=RI; G=1/R; Ohm’s Law is V=RI or I=GV.

Answer: C.

46. Power, absorbed by resistor, is equal to 400W, when current inside it is 5A. What is the resistance of the resistor? A. 6 Ω B. 10 Ω C. 12 Ω D.20Ω E. 16 Ω

Solution:

P=I²R; R=P/I²=400/25=16Ω

Answer: E.

47. Power p is defined as

A. dw/dt B. dw/dq C.dq/dt D. dq/dv E. dp/dt

Solution:

Power is defined as dw/dt and is a measure of the rate at which energy is being transferred.

Answer: A.

48. Proportionality applies when the input and output are ______ . Output_______ is not linearly related to the input _______ .