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1.

Determine the phase angle in the circuit shown below.(a) 56⁰(b) 56.5⁰(c) 57.5⁰(d) 57⁰I got this question in an online interview.This key question is from Parallel Circuits topic in portion Complex Impedence of Network Theory

Answer»

Correct CHOICE is (c) 57.5⁰

To elaborate: Phase ANGLE θ=tan^-1(R/Xc). Resistance R = 50Ω and capacitive REACTANCE Xc = 31.83Ω. So the phase angle in the circuit = tan^-1(50/31.83)=57.52⁰.

2.

Find the impedance in the circuit shown below.(a) 25(b) 26(c) 27(d) 28I got this question in an online interview.I need to ask this question from Parallel Circuits topic in chapter Complex Impedence of Network Theory

Answer»

The CORRECT answer is (c) 27

For explanation: Capacitive reactance XC = 1/2πfC = 1/(6.28×50×100×10^-6)=31.83Ω. Capacitive susceptance BC = 1/XC = 1/31.83 = 0.031S. Conductance G=1/R = 1/50 = 0.02S. TOTAL admittance Y=√(G^2+Bc^2)=√(0.02^2+0.031^2)=0.037S. Total IMPEDANCE Z = 1/Y = 1/0.037 = 27.02Ω.

3.

Find the phase angle θ in the circuit shown below.(a) 20.5⁰(b) 20⁰(c) 19.5⁰(d) 19⁰I have been asked this question in an interview for job.I need to ask this question from Parallel Circuits topic in portion Complex Impedence of Network Theory

Answer»

Correct CHOICE is (a) 20.5⁰

The best I can EXPLAIN: As IT = 0.77∠-20.5^o, the PHASE angle θ between the voltage and the CURRENT in the circuit is 20.5⁰.

4.

Find IT in the figure shown below.(a) 0.66∠-20.5⁰(b) 0.66∠20.5⁰(c) 0.77∠20.5⁰(d) 0.77∠-20.5⁰This question was posed to me by my school teacher while I was bunking the class.Question is from Parallel Circuits topic in section Complex Impedence of Network Theory

Answer»

Right ANSWER is (d) 0.77∠-20.5⁰

Explanation: The current lags behind the APPLIED VOLTAGE by 20.5⁰. TOTAL current IT = VS/ZT = 20/25.87∠20.5^o=0.77∠-20.5^o.

5.

Determine Z in the figure shown below.(a) 26∠-20.5⁰(b) 26∠20.5⁰(c) 25∠-20.5⁰(d) 25∠20.5⁰I had been asked this question during an online interview.This intriguing question comes from Parallel Circuits in chapter Complex Impedence of Network Theory

Answer»

The correct option is (b) 26∠20.5⁰

To explain: FIRST the inductive reactance is calculated. XL=6.28 X 50 x 0.1 = 31.42Ω. In figure the 10Ω resistance is in series with the PARALLEL combination of 20Ω and j31.42Ω. ZT = 10 + (20)(j31.42)/(20+j31.42)=24.23+j9.06=25.87∠20.5⁰.

6.

Determine total impedance in the circuit shown below.(a) 25∠-58.8⁰(b) 25∠-58.8⁰.(c) 26∠-58.8⁰.(d) 26∠58.8⁰.The question was posed to me by my school principal while I was bunking the class.Question is from Parallel Circuits topic in division Complex Impedence of Network Theory

Answer» RIGHT ANSWER is (c) 26∠-58.8⁰.

Easy explanation: The CURRENT lags BEHIND the voltage by 58.8⁰. Total impedance Z = VS/IT = 20∠0⁰ / 0.77∠-58.8⁰ = 25.97∠-58.8⁰Ω. So the total impedance in the circuit shown is 25.97∠-58.8⁰Ω.
7.

A 50Ω resistor is connected in parallel with an inductive reactance of 30Ω. A 20V signal is applied to the circuit. Find the line current in the circuit.(a) 0.77∠-58.8⁰(b) 0.77∠58.8⁰(c) 0.88∠-58.8⁰(d) 0.88∠58.8⁰This question was posed to me during an internship interview.Asked question is from Parallel Circuits topic in portion Complex Impedence of Network Theory

Answer»

Right answer is (a) 0.77∠-58.8⁰

To EXPLAIN I would SAY: SINCE the voltage across each element is the same as the applied voltage, the current in resistive branch is IR = VS/R = 20∠0⁰/50∠0⁰=0.4A. Current in the inductive branch is IL = VS/XL = 20∠0⁰/30∠90⁰= 0.66∠-90⁰. Total current is IT = 0.4-j0.66 = 0.77∠-58.8⁰.

8.

Determine the total impedance in the circuit.(a) 73.3∠33⁰(b) 83.3∠-33⁰(c) 83.3∠33⁰(d) 73.3∠-33⁰I got this question in unit test.Enquiry is from Parallel Circuits topic in section Complex Impedence of Network Theory

Answer»

Correct option is (B) 83.3∠-33⁰

To elaborate: Z = VS/IT = 20∠0⁰ / 0.24∠33⁰ = 83.3∠-33⁰Ω. The phase angle indicates that the TOTAL LINE current is 0.24 A and leads the voltage by 33⁰.

9.

Find the phase angle in the circuit shown below.(a) 31⁰(b) 32⁰(c) 33⁰(d) 34⁰This question was addressed to me in unit test.Question is from Parallel Circuits in division Complex Impedence of Network Theory

Answer»

The CORRECT choice is (c) 33⁰

For explanation: We OBTAINED IT = 0.24∠33⁰ A, the phase ANGLE between APPLIED voltage and current is 33⁰. The phase angle between the applied voltage and total current is 33⁰.

10.

A signal generator supplies a sine wave of 20V, 5 kHz to the circuit as shown. Determine total current IT.(a) 0.21∠33⁰(b) 0.22∠33⁰(c) 0.23∠33⁰(d) 0.24∠33⁰This question was addressed to me by my college professor while I was bunking the class.The doubt is from Parallel Circuits topic in portion Complex Impedence of Network Theory

Answer»

Correct OPTION is (d) 0.24∠33⁰

Explanation: Capacitive reactance = 1/(6.28×5×10^3×0.2×10^-6)=159.2Ω.CURRENT in the resistance BRANCH IR=VS/R=20/100 = 0.2A.Current in capacitive branch IC=VS/XC = 20/159.2 = 0.126A.Total current IT = (IR+j IC) A = (0.2+j0.13) A. In polar FORM, IT = 0.24∠33⁰ A.

11.

Find the voltage across the capacitor in the circuit shown below.(a) 7(b) 7.5(c) 8(d) 8.5I have been asked this question in examination.I would like to ask this question from Series Circuits topic in portion Complex Impedence of Network Theory

Answer»

Right option is (d) 8.5

The EXPLANATION: The VOLTAGE ACROSS the capacitor in the CIRCUIT is capacitor voltage = 2.66×10^-3×3184.7 =8.47V.

12.

In the circuit shown below determine the total impedance.(a) 161(b) 162(c) 163(d) 164This question was addressed to me in homework.The question is from Series Circuits in portion Complex Impedence of Network Theory

Answer»

Correct option is (b) 162

The BEST explanation: Reactance across capacitor = 1/(6.28×50×10×10^-6) = 318.5Ω.

Reactance across inductor = 6.28×0.5×50=157Ω. In RECTANGULAR form, Z = (10+j157-j318.5) Ω = (10-j161.5)Ω. Magnitude=161.8Ω.

13.

Find the current in the circuit shown below.(a) 0.1(b) 0.2(c) 0.3(d) 0.4This question was addressed to me during an interview for a job.My doubt is from Series Circuits topic in chapter Complex Impedence of Network Theory

Answer»

Right choice is (c) 0.3

The BEST explanation: The TERM current is the ratio of VOLTAGE to the IMPEDANCE. The current in the circuit is current I=VS/Z = 50/161.8 = 0.3A.

14.

Determine the voltage across the resistor in the circuit shown below.(a) 3(b) 4(c) 5(d) 6The question was posed to me in a national level competition.Query is from Series Circuits in division Complex Impedence of Network Theory

Answer»

Right ANSWER is (C) 5

Easy explanation: The VOLTAGE ACROSS the resistor in the CIRCUIT resistive voltage = 2.66×10^-3×3184.7 = 5.32V.

15.

Find the current I (mA) in the circuit shown below.(a) 2.66(b) 3.66(c) 4.66(d) 5.66The question was posed to me in semester exam.The doubt is from Series Circuits topic in portion Complex Impedence of Network Theory

Answer» RIGHT choice is (a) 2.66

The EXPLANATION: The term CURRENT is the ratio of voltage to the IMPEDANCE. The current I (mA) in the circuitis current I = VS / Z = 10/3760.6 = 2.66mA
16.

An AC voltage source supplies a 500Hz, 10V rms signal to a 2kΩ resistor in series with a 0.1µF capacitor as shown in the following figure. Find the total impedance.(a) 3750.6Ω(b) 3760.6Ω(c) 3780.6Ω(d) 3790.6ΩThe question was asked by my college director while I was bunking the class.The above asked question is from Series Circuits in chapter Complex Impedence of Network Theory

Answer»

The correct choice is (b) 3760.6Ω

The BEST I can explain: The capacitive reactance XC = 1/2πfC = 1/(6.28×500×0.1×10^-6))=3184.7Ω. In rectangular form, X = (2000-j3184.7)Ω. Magnitude = 3760.6Ω.

17.

Determine the source voltage if voltage across resistance is 70V and the voltage across inductor is 20V as shown in the figure.(a) 71(b) 72(c) 73(d) 74I had been asked this question in an interview for internship.I need to ask this question from Series Circuits in section Complex Impedence of Network Theory

Answer»

Right choice is (C) 73

Explanation: If voltage ACROSS resistance is 70V and the voltage across inductor is 20V, SOURCE voltage Vs=√(70^2+20^2) = 72.8≅73V.

18.

Determine the phase angle in the circuit shown below.(a) 58(b) 68(c) -58(d) -68This question was addressed to me in unit test.I need to ask this question from Series Circuits topic in chapter Complex Impedence of Network Theory

Answer»

The correct ANSWER is (c) -58

To ELABORATE: The phase ANGLE in the CIRCUIT is phase angle θ = tan^-1⁡(-XC/R) =tan^-1⁡((-3184.7)/2000)=-57.87^o≅-58^o.

19.

Find the phase angle in the circuit shown below.(a) 15(b) 16(c) 17(d) 18This question was addressed to me in quiz.The above asked question is from Series Circuits in portion Complex Impedence of Network Theory

Answer» CORRECT choice is (b) 16

Explanation: The phase angle is the angle between the source voltage and the current. Phase angle θ=tan^-1(VL/VR). The VALUES of VL = 20V and VR = 70V. On SUBSTITUTING the values in the equation, phase angle in the circuit = tan^-1(20/70)=15.94^o≅ 16^o.
20.

In the circuit shown below, find voltage across inductive reactance.(a) 9.5(b) 10(c) 9(d) 10.5I had been asked this question by my college director while I was bunking the class.This interesting question is from Series Circuits in section Complex Impedence of Network Theory

Answer»

Right OPTION is (a) 9.5

Explanation: Voltage ACROSS inductor = IXL. The values of I = 3.03 mA and XL = 10000Ω. On SUBSTITUTING the values in the EQUATION, the voltage across inductor = 3.03×10^-3×1000 = 9.51V.

21.

In the circuit shown below, find the voltage across resistance.(a) 0.303(b) 303(c) 3.03(d) 30.3The question was asked by my school principal while I was bunking the class.This intriguing question comes from Series Circuits topic in section Complex Impedence of Network Theory

Answer»

The CORRECT choice is (c) 3.03

Easy explanation: VOLTAGE across resistance = IR. The values of I = 3.03 mA and R = 10000Ω. On SUBSTITUTING the values in the equation, the voltage across resistance = 3.03 x 10^-3×1000 = 3.03V.

22.

If we apply a sinusoidal input to RL circuit, the current in the circuit is __________ and the voltage across the elements is _______________(a) square, square(b) square, sinusoid(c) sinusoid, square(d) sinusoid, sinusoidThe question was posed to me by my school principal while I was bunking the class.The origin of the question is Series Circuits in chapter Complex Impedence of Network Theory

Answer» CORRECT choice is (d) sinusoid, sinusoid

The explanation: If we apply a sinusoidal input to RL circuit, the current in the circuit is SQUARE and the voltage across the ELEMENTS is sinusoid. In the ANALYSIS of the RL series circuit, we can find the impedance, current, phase ANGLE and voltage drops.
23.

Find the phase angle θ in the circuit shown below.(a) 62.33⁰(b) 72.33⁰(c) 82.33⁰(d) 92.33⁰The question was asked in an interview for internship.My question is from Series Circuits topic in portion Complex Impedence of Network Theory

Answer» RIGHT answer is (B) 72.33⁰

The best I can explain: Phase angle θ = tan^-1⁡(XL/R). The values of XL, R are XL = 3140Ω and R = 1000Ω. On SUBSTITUTING the values in the equation, phase angle θ=tan^-1⁡(3140/1000)=72.33⁰.
24.

Find the current I (mA) in the circuit shown below.(a) 3.03(b) 30.3(c) 303(d) 0.303I got this question during an interview.This is a very interesting question from Series Circuits topic in chapter Complex Impedence of Network Theory

Answer» RIGHT OPTION is (a) 3.03

For explanation: Total IMPEDANCE Z = (1000+j3140) Ω. Magnitude = 3295.4Ω

Current I=Vs/Z = 10/3295.4=3.03mA.
25.

The circuit shown below consists of a 1kΩ resistor connected in series with a 50mH coil, a 10V rms, 10 KHz signal is applied. Find impedance Z in rectangular form.(a) (1000+j0.05) Ω(b) (100+j0.5) Ω(c) (1000+j3140) Ω(d) (100+j3140) ΩThe question was posed to me in an interview for job.My question is taken from Series Circuits in section Complex Impedence of Network Theory

Answer»

Correct ANSWER is (c) (1000+j3140) Ω

To elaborate: Inductive Reactance XL = ωL = 2πfL = (6.28)(10^4)(50×10^-3) = 3140Ω. In RECTANGULAR form, total IMPEDANCE Z = (1000+j3140) Ω.

26.

The angle between resistance and impedance in the circuit shown below.(a) tan^-11/ωRC(b) tan^-1⁡C/ωR(c) tan^-1⁡R/ωC(d) tan^-1⁡ωRCThis question was addressed to me in an interview for job.I would like to ask this question from Impedence Diagram topic in division Complex Impedence of Network Theory

Answer»

Correct CHOICE is (a) tan^-11/ωRC

Best EXPLANATION: The angle between RESISTANCE and IMPEDANCE in the circuit shown above tan^-1⁡1/ωRC. The angle between resistance and impedance is the phase angle between the applied voltage and current in the circuit.

27.

The magnitude of the impedance of the circuit shown below is?(a) √(R+1/ωC)(b) √(R-1/ωC)(c) √(R^2+(1/ωC)^2)(d) √(R^2-(1/ωC)^2)I had been asked this question in an online quiz.Origin of the question is Impedence Diagram in section Complex Impedence of Network Theory

Answer»

The correct answer is (c) √(R^2+(1/ωC)^2)

For EXPLANATION: The magnitude of the IMPEDANCE of the circuit shown above is √(R^2+(1/ωC)^2). Here the impedance is the vector sum of the RESISTANCE and the CAPACITIVE reactance.

28.

The impedance of the circuit shown below is?(a) R + jωC(b) R – jωC(c) R + 1/jωC(d) R – 1/jωCThis question was addressed to me in an interview.This question is from Impedence Diagram in portion Complex Impedence of Network Theory

Answer»

Right option is (C) R + 1/jωC

The best I can explain: The IMPEDANCE of the circuit SHOWN above is R + 1/jωC. Here the impedance Z consists RESISTANCE which is real part and capacitive reactance which is imaginary part of the impedance.

29.

The voltage function v(t) in the circuit shown below is?(a) v(t) = e^-tjω(b) v(t) = e^tjω(c) v(t) = Vme^tjω(d) v(t) = Vme^-tjωThis question was addressed to me in an internship interview.This interesting question is from Impedence Diagram topic in division Complex Impedence of Network Theory

Answer»

Right answer is (C) v(t) = Vme^tjω

To explain: If we consider the RC series circuit and APPLY the complex FUNCTION v(t) to the circuit then voltage function is GIVEN by v(t) = Vme^tjω.

30.

The phase angle between current and voltage in the circuit shown below is?(a) tan^-1⁡ωL/R(b) tan^-1⁡ωR/(c) tan^-1⁡R/ωL(d) tan^-1⁡L/ωRThe question was asked during an online exam.The question is from Impedence Diagram topic in chapter Complex Impedence of Network Theory

Answer»

The correct ANSWER is (a) tan^-1⁡ωL/R

The best I can explain: The angle between impedance and REACTANCE is the phase angle between the CURRENT and voltage applied to the CIRCUIT. θ=tan^-1⁡ωL/R

31.

What is the magnitude of the impedance of the following circuit?(a) √(R+ωL)(b) √(R-ωL)(c) √(R^2+(ωL)^2)(d) √(R^2-(ωL)^2)This question was addressed to me in my homework.The question is from Impedence Diagram topic in portion Complex Impedence of Network Theory

Answer»

The correct option is (c) √(R^2+(ωL)^2)

For explanation: Complex IMPEDANCE is the total opposition offered by the circuit ELEMENTS to ac current and can be displayed on the complex PLANE. The magnitude ofthe impedance of the circuit is √(R^2+(ωL)^2).

32.

The impedance of the circuit shown below is?(a) R + jωL(b) R – jωL(c) R + 1/jωL(d) R – 1/jωLThis question was posed to me in a job interview.My question is taken from Impedence Diagram in division Complex Impedence of Network Theory

Answer» RIGHT OPTION is (a) R + jωL

Easy explanation: Impedance is DEFINED as he ratio of the voltage to current function. The impedance of the circuit Z= Vme^tjω/((Vm/(R+jωL)) e^tjω)=R+jωL.
33.

The current i(t) in the circuit shown below is?(a) i(t)=(Vm/(R-jωL))e^tjω(b) i(t)=(Vm(R+jωL)) e^tjω(c) i(t)=(Vm(R-jωL)) e^tjω(d) i(t)=(Vm/(R+jωL)) e^tjωThe question was asked during an interview.This interesting question is from Impedence Diagram in chapter Complex Impedence of Network Theory

Answer» RIGHT CHOICE is (d) i(t)=(VM/(R+jωL)) e^tjω

To EXPLAIN: i(t)=IM e^tjω. Vm e^tjω=RIm e^tjω+Ld/dt (Im e^tjω). Vme^tjω=RIm e^tjω+L Im(jω)e^tjω. Im = Vm/(R+jωL). i(t)=(Vm/(R+jωL)) e^tjω.
34.

The voltage function v(t) in the circuit shown below is?(a) v(t) = Vm e^-tjω(b) v(t) = Vme^tjω(c) v(t) = e^tjω(d) v(t) = e^-tjωI have been asked this question in an internship interview.I need to ask this question from Impedence Diagram topic in chapter Complex Impedence of Network Theory

Answer»

Correct choice is (b) V(t) = Vme^tjω

For EXPLANATION: The VOLTAGE function v(t) in the circuit is a complex function and is given by v(t) = VM e^tjω=Vm(cosωt+jsinωt).

35.

Impedance is a complex quantity having the real part as _______and the imaginary part as ______(a) resistance, resistance(b) resistance, reactance(c) reactance, resistance(d) reactance, reactanceI have been asked this question in exam.My query is from Impedence Diagram topic in division Complex Impedence of Network Theory

Answer»

Correct answer is (B) resistance, reactance

Explanation: Almost all electric circuits OFFER impedance to the FLOW of CURRENT. Impedance is a complex quantity having the REAL part as resistance and the imaginary part as reactance.