EE-1151 CT Submitted Copy

EE 1151 –CIRCUIT THEORY

KINGSCOLLEGE OF ENGINEERING

DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING

QUESTION BANK

NAME OF THE SUBJECT: EE 1151 – CIRCUIT THEORY

YEAR / SEM : I / II

UNIT – I

BASIC CIRCUITS ANALYSIS

PART – A (2-MARKS)

1. State Ohm’s law.

The potential difference across any two ends of a conductor is directly proportional to the current flowing between the two ends provided the temperature of the conductor remains constant.

Mathematically , (V / I) = R

2. Mention the limitations of Ohm’s Law.

i) Ohm’s law cannot be applied to non-metallic conductors.ii) It cannot be applied to non-linear devices such as Zener diode, Voltage

regulator (VR) tubes etc.,iii) Ohm’s law holds good only for constant temperature. If the temperature

changes, this law cannot be applied.

3. State Kirchhoff’s voltage law.

The algebraic sum of electromotive forces plus the algebraic sum of voltages across the impedances, in any closed circuit is equal to zero.

4. State Kirchhoff’s Current law.

The algebraic sum of the currents meeting at a junction (node) is equal to zero.

KINGS COLLEGE OF ENGINEERING, PUNALKULAM 1


5. State two salient points of a series combination of resistance.

i) Current is same and voltage is distributedii) The total resistance is greater than the individual resistance

6. State two salient points of a parallel combination of resistance.

i) Voltage is same across all individual resistanceii) Current is divided, inversely proportional to the resistors.iii) The total resistance is less than the least.

7. Give two applications of both series and parallel combination.

For Series combination:

i) A fan regulator connected in series with the fanii) Decoration lights

For Parallel combination:

i) Electrical wiring in cinema hallsii) House wiring

8. Define an ideal voltage source.

For an ideal voltage, source impedance is zero. Such voltage source gives a constant voltage V irrespective of current drawn from it.

9. Define an ideal current source.

For an ideal current source, source impedance is infinite. Such an ideal current source gives a constant current irrespective of voltage across it.

10.Explain how voltage source with a source resistance can be converted into an equivalent current source.

Let the voltage source have a voltage of V volts and resistance of R. R is in series with source. Its equivalent current source will have a current in parallel with resistance R. Here I = V / R

11. Name the four different types of dependent sources in electric circuits.

i) Voltage – controlled voltage source (VCVS)ii) Voltage – controlled current source (VCCS) iii) Current – controlled voltage source (CCVS) iv) Current - controlled current source (CCCS)



12. Define R.M.S value.

The steady current which when flows through a given resistor for a given resistor for a given time produces the same amount of heat as is produced by the alternating current when flows through the same resistor for the same time is called RMS value or effective value of the alternating current.

13. State the advantages of sinusoidal alternating quantity.

i) Iron loss and copper losses are low in AC rotating machines and transformers, which are operated on sinusoidal voltage. Hence there will be an improving efficiency.ii) There will be less interference to near by telephone lines.iii) The sinusoidal voltage produces less disturbance in the electrical circuit.

14. What is a phasor?

It is a rotating vector

15. What is meant by linear and nonlinear elements?

Linear elements shows linear characteristic of voltage Vs Current.

Nonlinear element the Current passing through it does not change linearly with thelinear change in applied voltage at a particular frequency

16. What is meant by active and Passive elements?

If a circuit element has the capability of enhancing the energy level of a signal passing thorough it is called an active element.

Passive elements do not have any intrinsic means of signal boosting.

17. What is meant by Unilateral and bi-lateral element?

If the magnitude of the current passing through an element is affected due to change in the polarity of the applied voltage is called Uni-lateral elements.If the current magnitude remains the same even if the applied EMFs polarity is changed is called bilateral elements.



PART – B

1. Find the current through each branch by network reduction technique. (16)

2. Calculate a) the equivalent resistances across the terminals of the supply, b) total current supplied by the source and c) power delivered to 16 ohm resistor in the circuit shown in figure. (16)

3. In the circuit shown, determine the current through the 2 ohm resistor and the total current delivered by the battery. Use Kirchhoff’s laws. (16)



4. (a) Determine the current through 800 ohm resistor in the network shown in figure. (8)

(b) Find the power dissipated in 10 ohm resistor for the circuit shown in figure. (8)

5. (a) In the network shown below, find the current delivered by the battery. (10)

(b) Discuss about voltage and current division principles. (6)

6. Explain with relevant diagrams:a) Kirchoff laws. (5)b) Dependent sources (3)c) Source transformations (4)d) Voltage division and current division rule (4)



7. (a) Determine the value of V2 such that the current through the impedance (3+j4) ohm is zero. (8)

(b) Find the current through branch a-b using mesh analysis shown in figure below. (8)

8. Determine the mesh currents I1 and I2 for the given circuit shown below (16)

9. Find the node voltages V1 and V2 and also the current supplied by the source for the circuit shown below. (16)



10. Find the nodal voltages in the circuit of figure. (16)

11. (a) Using the node voltage analysis, find all the node voltages and currents in 1/3 ohm and 1/5 ohm resistances of figure. (8)

(b) For the mesh-current analysis, explain the rules for constructing mesh impedance matrix and solving the matrix equation [Z]I = V. (8)

12.Solve for V1 and V2 using nodal method. Let V = 100V. (16)

13.Using Mesh analysis, find current through 4 ohm resistor. (16)



14.Use nodal voltage method to find the voltages of nodes ‘m’ and ‘n’ and currents through j2 ohm and –j2 ohm reactance in the network shown below. (16)

15.For the circuit shown find the current I flowing through 2 ohm resistance using loop analysis. (16)

UNIT – II

NETWORK REDUCTION AND NETWORK THEOREMS FOR DC AND AC CIRCUITS


1. State Superposition theorem.

In a linear circuit containing more than one source, the current that flows at any point or the voltage that exists between any two points is the algebraic sum of the currents or the voltages that would have been produced by each source taken separately with all other sources removed.

2. State Thevenin’s theorem.

It states that any linear bilateral network can be replaced by a single voltage source, Vth , in series with a single impedance, Zth

3. State Norton’s theorem.

It states that any linear bilateral network can be replaced by a single Current source, IN, in parallel with a single impedance, Zth

4. State Maximum power transfer theorem.



For DC Circuits : Maximum power will be delivered from a voltage source to load, when the load resistance is equal to the internal resistance of the source.

For AC Circuits : Maximum Power is transferred to load impedance if the Load impedance is the complex conjugate of the source impedance.

5. State reciprocity theorem.

In a Linear bilateral network a voltage source V volts in a branch gives rise to a current I, in another branch. If V is applied in the second branch, the current in the first branch will be I. This V/I is called transfer impedance or resistance.

6. Write some applications of Maximum power transfer theorem.

i) In communication circuitsii) In Power networks

7. A voltage source has internal impedance (4+j5) ohm. Find the load impedance for maximum power transfer.

The load impedance is (4-j5) ohm. Because for maximum power transfer the load impedance is complex conjugate of source impedance.

8. Given that the resistors Ra, Rb and Rc are connected electrically in star. Write the equations for resistors in equivalent delta.

RAB = (RARB + RARC + RBRC) / RC

RBC = (RARB + RARC + RBRC) / RA

RCA = (RARB + RARC + RBRC) / RB

9. Three equal resistors each of R ohms are connected in star. Find the value of resistors in the equivalent delta.

RAB = RBC = RCA = 3R

10.Three resistors Rab, Rbc and Rca are connected in delta. Write the expression for resistors in equivalent star.

RA = RABRCA / ΣRAB

RB = RABRBC / ΣRAB

RC = RBCRCA / ΣRAB



11.Three resistors, each of value R ohms are connected in delta. Find the value of resistors in its equivalent star.

RA = RB = RC = (R / 3)

PART – B

1. (a) Find the value of R and the current flowing through it in the circuit shown when the current in the branch OA is zero. (8)

(b) Determine the Thevenin’s equivalent for the figure (8)

2. Derive expressions for star connected arms in terms of delta connected arms and delta connected arms in terms of star connected arms. (16)

3. Determine Thevenin’s equivalent across the terminals AB for the circuit shown in figure below. (16)



4. Find the Thevenins’s equivalent circuit of the circuit shown below, to left of the terminals ab. Then find the current through RL = 16 ohm and 36 ohm. (16)

5. (a) Find the current through branch a-b network using Thevenin’s theorem. (8)

(b) Find the current in each resistor using superposition principle of figure. (8)

6. (a) Determine the Thevenin’s equivalent circuit. (8)



(b) Determine the equivalent resistance across AB of the circuit shown in the figure below. (8)

7. For the circuit shown, use superposition theorem to compute current I. (16)

8. (a)Compute the current in 23 ohm resistor using super position theorem for the circuit shown below. (8)

(b) Find the equivalent resistance between B and C in figure (8)



9. Using superposition theorem calculate current through (2+j3) ohm impedance branch of the circuit shown. (16)

10. (a) For the circuit shown, determine the current in (2+j3) ohm by using superposition theorem. (8)

(b) State and prove Norton’s theorem. (8)

11.(a) Find the value of RL so that maximum power is delivered to the load resistance shown in figure. (8)



(b) State and explain reciprocity theorem. (8)

12.Determine the maximum power delivered to the load in the circuit. (16)

13.Find the value of impedance Z so that maximum power will be transferred from source to load for the circuit shown. (16)

14. (a) State and explain maximum power transfer theorem for variable Pure resistive load. (8)

(b) Using Norton’s theorem, find current through 6 ohm resistance shown in figure.

(8)

UNIT – III

RESONANCE AND COUPLED CIRCUITS


1. Define quality factor.



The quality factor is defined as the ratio of maximum energy stored to the energy dissipated in one period.

2. What are half power frequencies?

In RLC circuits the frequencies at which the power is half the max /min power are called half power frequencies.

3. Define selectivity.

It is defined as the ratio of bandwidth and resonant frequency.

4. Write the characteristics of series resonance.

i) At resonance impedance is minimum and equal to resistance therefore current is max.ii) Before resonant frequency the circuit behave as capacitive circuit and above resonant frequency the circuit will behave as inductive circuit.iii) At resonance the magnitude of voltage across inductance and capacitance will be Q times the supply voltage but they are in phase opposition.

5. What is anti resonance?

In RLC parallel circuit the current is min at resonance whereas in series resonance the current is max. therefore the parallel resonance is called anti resonance.

6. Write the characteristics of parallel resonance.

i) At resonance admittance is min and equal to conductance therefore the current is min.ii) Below resonant frequency the circuit behave as inductive circuit and above resonant frequency the circuit behave as capacitive circuit.iii) At resonance the magnitude of current through inductance and capacitance will be q times the current supplied by the source but they are in phase opposition.

7. What is Band width and Selectivity ?

The frequency band within the limits of lower and upper half frequency is called Bandwidth, B.W = f2-f1

Selectivity is the ratio of fr to the B.W, Selectivity = fr / (f2-f1)

8. Mention the Properties of a series RLC circuit.

i) The applied voltage and the resulting current are in phase, which also means that the p.f of RLC circuit is unity.

ii) The net reactance is zero at resonance and the impedance does have the resistive part only.



iii) The current in the circuit is max: and is V/R amperesiv) At resonance the circuit has got minimum impedance and max: currentv) Frequency of resonance is given by fr = 1/(2LC)

9. Mention the Properties of a parallel RLC circuit.

i) PF is unityii) Current at resonance is (V/(L/RC)) and is in phase with the applied voltage.

The value of current at resonance is minimum.iii) Net impedance at resonance is max: & is equal to L/RCiv) The admittance is min: and the net susceptance is zero at resonance.

10. What is resonance?

An AC Circuit comprising of R, L and C is said to be in resonance when the applied voltage and the source current are in phase. Thus, at resonance the power factor of the circuit is unity and the circuit acts as purely resistive circuit.

11. What are coupled circuits?

It refers to circuits involving elements with magnetic coupling. If the flux produced by an element of a circuit links other elements of the same circuit then the elements are said to be magnetic coupling.

12. What are coupled coils?

When two or more coils are linked by magnetic flux, then the coils are called coupled coils.

13. Define self-inductance.

When permeability is constant the self inductance of a coil is defined as the ratio of flux linkage and current.

14. Define mutual inductance.

When permeability is constant the mutual inductance between two coupled coils is defined as the ratio of flux linkage in one coil due to common flux and current through another coil.

15. Define coefficient of coupling.

In coupled coils the coefficient of coupling is defined as the fraction of the total flux produced by one coil linking another coil.



K = M / √L1L2

16. What is DOT convention?

The sign of mutual induced emf depends on the winding sense and the current through the coil. The winding sense is decided by the manufacturer and to inform the user about the winding sense a dot is placed at one end of each coil. When current enter at dotted end in one coil then the mutual induced emf in the other coil is positive at dot end.

17. State dot rule for coupled coils.

a. It states that in coupled coils current entering at the dotted terminal of one coil induce an emf in second coil which is +ve at dotted terminal of second coil.b. Current entering at the un dotted terminal of one coil induce an emf in second coil which is +ve at un dotted terminal of second coil.

PART – B

1. Derive bandwidth for a series RLC circuit as a function of resonant frequency. (16)

2. (a) For the circuit below, find the value of ω so that current and source emf are in phase. Also find the current at this frequency. (8)

(b) Discuss the characteristics of parallel resonance of a circuit having G,L and C.(8)

3. (a) A Pure resistor, a pure capacitor and a pure inductor are connected in parallel across a 50Hz supply, find the impedance of the circuit as seen by the supply. Also find the resonant frequency. (8)(b) When connected to a 230V, 50Hz single phase supply, a coil takes 10kVA and 8kVAR. For this coil calculate resistance, inductance of coil and power consumed.(8)

4. (a) Explain in detail about Single tuned circuits. (8)(b) A series RLC circuit has Q = 75 and a pass band (between half power frequencies) of 160 Hz. Calculate the resonant frequency and the upper and lower frequencies of the pass band. (8)



5. (a) Explain and derive the relationships for bandwidth and half power frequencies of RLC series circuit. (8)(b) Determine the quality factor of a coil R = 10 ohm, L = 0.1H and C = 10µF (8)

6. A series RLC circuit has R=20 ohm, L=0.005H and C = 0.2 x 10-6 F. It is fed from a 100V variable frequency source. Find i) frequency at which current is maximum ii) impedance at this frequency and iii) voltage across inductance at this frequency.(16)

7. A series RLC circuit consists of R=100 ohm, L = 0.02 H and C = 0.02 microfarad. Calculate frequency of resonance. A variable frequency sinusoidal voltage of constant RMS value of 50V is applied to the circuit. Find the frequency at which voltage across L and C is maximum. Also calculate voltage across L and C is maximum. Also calculate voltages across L and C at frequency of resonance. Find maximum current in the circuit. (16)

8. In the parallel RLC circuit, calculate resonant frequency, bandwidth, Q-factor and power dissipated at half power frequencies. (16)

9. (a) For the given circuit constants, find (a) Mutual Inductance (b) Find equivalent inductance for all the combination L1 = 0.02H , L2 = 0.01H and k = 0.5. (8)

(b) Calculate the mutual inductance of two coils of self-inductances 100µH and 240µH, which are connected in series to yield a total inductance of 146µH. (4)(c) Two perfectly coupled coils each of 1H self-inductance are connected in parallel so as to aid each other. Calculate the effective inductance. (4)

10.Three similar coils are wound on a long common core in such a way that the voltage of mutual inductance between each set of coils is positive. The self-inductance of each coil is 0.2H. The effective inductance of the first two in series is 0.6H and of all the three in series is 1H. When the terminals of the first coil are interchanged, the effective inductance of the three coils in series becomes 0.5 H. Determine the co-efficient of coupling between each set of coils. (16)

11.What is mutual inductance? Derive an expression for the mutual inductance between two magnetically coupled coils having self-inductances L1 and L2

respectively. (16)

12.A coil of inductance 100µH and of self-inductance 5pF is magnetically coupled to another coil of inductance 200µH and of self-inductance 10pF. The co-efficient of



coupling between the coil is 0.1.Calculate the effective mutual inductance between them at 1 MHz. (16)

UNIT – IV

TRANSIENT RESPONSE OF DC AND AC CIRCUITS


1. What is transient?

The state of the circuit from the instant of switching to attainment of steady state is called transient state.

2. Why transients occur in electric circuits?

The inductance will not allow sudden change in current and the capacitance will not allow sudden change in voltage. Hence in inductive and capacitive circuits transient occurs during switching operation.

3. What is free and forced response?

The response of the circuit due to stored energy alone is called free response. The response of a circuit due to an external source is called forced response.

4. What is complementary function?

The part of the response which becomes zeroes t tends to infinite is called complementary function.

5. What is particular solution?

The part of the solution which attains a steady value as t tents to infinity is called particular solution.



6. Define time constant of RL circuit.

The time constant of RL series circuit is defined as the period during which the current rises to 63.2 % of its final value.

7. Define time constant of RC circuit.

The time constant RC circuit is defined as the time during which the current falls to 36.8 % of initial current.

8. What is damping ratio?

The ratio of resistance of the circuit and resistance for critical damping is called damping ratio.

9. What is critical damping.?

It is the condition of the circuit at which the oscillations in the response are just eliminated. This is possible by increasing the value of resistance in the circuit.

10. What is critical resistance?

It is the value of the resistance of the circuit to achieve critical damping.11. What is natural and damped frequency?

a. The response of a circuit is completely oscillatory with a frequency in the absence of resistance and this frequency is called natural frequency.b. The response of under damped circuit is oscillatory with a frequency and these oscillations are damped as t tends to infinity. The frequency of response is called damped frequency.

12. What is an initial condition?

Initial conditions of a network are the values of currents and voltage just before switching. The instant just before switching is denoted by t = 0 -. The instant exactly switching is denoted by t = 0 and the instant just after switching is denoted by t = 0+.

13. What is the steady state value?

A Circuit consisting of constant sources is said to be in steady state if the voltages and currents do not change with time.

14. What are critical frequencies? Why they are so called?

The critical frequencies are poles and zeros. They are so called because zeros of network function give the values of s which make the function zero and poles of a



network function give the values of s which make the function infinite. At every other frequency, the network function has a finite non-zero value.

15. Distinguish between steady state and transient response.

S.NO STEADY STATE RESPONSE TRANSIENT RESPONSE1 Amplitude will not change Amplitude may change2 Frequency will not change Frequency will change

3Constant voltage and current with time in steady state

Change from one steady state to another

4 Algebraic equations are used Integro-differential equations are used.

PART – B

1. In the circuit of the figure shown below, find the expression for the transient current and the initial rate of growth of the transient current (16)

2. In the circuit shown in figure, switch S is in position 1 for a long time and brought to position 2 at time t=0. Determine the circuit current. (16)

3. A resistance R and 2 microfarad capacitor are connected in series across a 200V direct supply. Across the capacitor is a neon lamp that strikes at 120V. Calculate R to make the lamp strike 5 sec after the switch has been closed. If R = 5Megohm, how long will it take the lamp to strike? (16)

4. A Series RLC circuits has R=50 ohm, L= 0.2H, and C = 50 microfarad. Constant voltage of 100V is impressed upon the circuit at t=0. Find the expression for the transient current assuming initially relaxed conditions. (16)



5. A Series RLC circuits with R=300 ohm, L=1H and C=100x10-6 F has a constant

voltage of 50V applied to it at t= 0. Find the maximum value of current ( Assume zero initial conditions) (16)

6. For a source free RLC series circuit, the initial voltage across C is 10V and the initial current through L is zero. If L = 20mH, C=0.5 microfarad and R=100 ohm. Evaluate i(t). (16)

7. Derive an expression for current response of RLC series circuit transient. (16)

8. Derive an expression for current response of RL and RC series circuit transients.(16)

9. A step voltage V(t) = 100 u(t) is applied to a series RLC circuit with L=10H, R=2ohm and C= 5F. The initial current in the circuit is zero but there is an initial voltage of 50V on the capacitor in a direction which opposes the applied source. Find the expression for the current in the circuit. (16)

10.For the circuit shown in figure, find the voltage across the resistor 0.5 ohm when the switch, S is opened at t=0. Assume that there is no charge on the capacitor and no current in the inductor before switching. (16)

11. In the circuit shown in figure, find the current i. Assume that initial charge across the capacitor is zero. (16)



12. In the circuit shown in figure, the switch is closed at time t=0. Obtain i(t). Assume zero current through inductor L and zero charge across C before closing the switch.

(16)

UNIT – V

ANALYSING THREE PHASE CIRCUITS


1. What is balanced voltage?

In poly phase system when the magnitude of phase voltages are equal and the phase difference between consecutive phasors are equal then the voltages are called balanced voltages.

2. What are balanced impedance?

When the impedances of all the phases of a three-phase load are equal then the impedances are called balanced impedance.

3. What is phase sequence?

In a set of rotating phasors, the order of reaching reference point is called phase sequence.

4. Write the relation between the line and phase value of voltage and current in a balanced star connected load.

In star connected load the line current and phase current are same. In balanced star connected system the magnitude of line is √3 times the phase voltage and it leads the phase voltage by 30degree.



5. Write the relation between the line and phase voltage of voltage current in a balanced delta connected load.

In a delta connected system the line voltage and phase voltage are same. In balanced delta connected load the magnitude of line current is √3 times the phase current and it lags the phase current by 30 degree.

6. What is neutral shift voltage?

In three wire star connected load, the load neutral is not connected to source neutral. Therefore when the load is unbalanced the load neutral will not be at zero potential. The voltage of load neutral with respect to source neutral is called neutral shift voltage.

7. Write the relation between the power factor and wattmeter readings in two-wattmeter method of power measurement.

a. When the wattmeter readings are equal the power factor is unity.b. When one of the wattmeter reading is zero the power factor is 0.5.c. When both the readings are +ve the pf will be greater than 0.5.

8. In three phase circuit, what do you mean by balanced load?

When the loads in all the phases are identical, it is called balanced load.

9. When is a three phase supply system called balanced supply system?

When all the three phase voltages are equal in magnitude and displaced by 120º in space, the supply system is called three phase balanced system.

10. List any two advantages of 3-phase system over 1-phase system.

i) For the same size of an ac generator, output of 3-phase generator is double that of 1-phase generator.

ii) Three phase motors are self-starting, whereas the single phase induction motors are not.

iii) Fault location is easier in three phase motor than that in single phase motor.

PART – B

1. With a neat circuit and phasor diagram explain the three phase power measurement by two wattmeter method and also derive the expression for Power Factor. (16)



2. (a) A symmetrical three phase 400V system supplies a balanced delta connected load. The current in each branch circuit is 20A and phase angle 40° (lag) calculate the line current and total power. (8)

(b) A three phase delta connected load has Zab = (100+j0) ohms, Zbc = (-j100) ohms and Zca = (70.7 =j70.7) ohms is connected to a balanced 3 phase 400V supply. Determine the line currents Ia,Ib and Ic. Assume the phase sequence abc. (8)

3. (a) A balanced three phase star connected load with impedance 8+j6 ohm per phase is connected across a symmetrical 400V three phase 50Hz supply. Determine the line current, power factor of the load and total power. (8)

(b) An alternating current is expressed as i=14.14 sin 314t. Determine rms current, frequency and instantaneous current when t =0.02ms. (8)

4. (a) A balanced star connected load of 4+j3 ohm per phase is connected to a 400V, 3 phase, 50Hz supply. Find the line current, power factor ,power, reactive volt ampere and total volt ampere. (8)

(b) A Voltage source 100V with resistance of 10 ohms and inductance 50 mH, a capacitor 50 microfarad are connected in series. Calculate the impedance when the frequency is (i) 50HZ (ii) 500Hz (iii) the power factor at 100Hz. (8)

5. (a) Three impedances Z1 = 3∟45° ohm, Z2 = 10√2∟45° ohm, Z3 = 5∟-90° ohm are connected in series. Calculate applied voltage if voltage across Z1 = 27∟-10° V. (8)

(b) A delta connected load as shown in figure is connected across 3 phase 100 volt supply. Determine all line currents. (8)



6. Three load impedances are connected in star to a three-phase supply with a line voltage of 208V. The phase sequence is ABC. Given ZA = 10∟0° Ω, ZB = 15∟0° Ω and ZC = 10∟-30° Ω. Calculate the three line currents IA, IB and IC and the voltage across the load impedances. (16)

7. Three identical coils each having a resistance of 20 Ω and a reactance of 20 Ω are connected in i) Star ii) Delta across 440 V, 3 phase supply. Calculate for each case, line current and reading in each of the wattmeters connected to measure power. (16)

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EE-1151 CT Submitted Copy

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