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Circuit Theory Question

Bank, 2 marks with answers

BASIC CIRCUIT ANALYSIS

UNIT-I

PART-A

1. What is a graph of network?

When all elements in a network are replaced by lines with circles of dos at both ends.

2. What is tree of a network?

It is an interconnected

given graph.

open set of branches which include all the nodes of the

3. Give the properties of tree in a graph.

It consists of all the nodes of the graph

If the graph has N no of nodes the tree will have N-I branches

There will be no closed path in the tree

There can be many possible different trees for a given graph depending on the no of

nodes and branches.

4. Define Ohms Law.

The potential difference cross any two ends of a conductor is directly proportional to

the current flowing between

remains constant.

5. Define Quality factor.

the two ends provided the temperature of the conductor

The quality factor is defined as the ratio of maximum energy stored to the energy

dissipated in one period.

6. What are half power frequencies?

In RLC circuits the frequ ncies at which the power is half the max/min power arecalled half power frequencies.

7. Define selectivity.

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

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8. Write the characteristics of series resonance.

At resonance impedance in min and equal to resistance therefore current is max.

Before resonant frequency the circuit behaves as capacitive circuit and above resonant

frequency the circuit will behave as inductive circuit. At resonance the magnitude of

voltage across the inductance and capacitance will be Q times the supply voltage but they

are in phase opposition.

9. 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.

10. Write the characteristics of parallel resonance.

At resonance admittance in min and equal to conductance therefore the current is

min.

Below resonant frequency the circuits behave as inductive circuit and aboveresonant frequency the circuit behaves as capacitive circuit.

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.

11. Define KCL

KCL states that the algebraic sum of currents in node is zero.

12. Define KVL

KVL states that the algebraic sum of voltages in a closed path is zero.

13. What is meant by linear and nonlinear elements?

Linear element shows the linear characteristics of voltage Vs current.

Nonlinear element the current passing through it does not change linearity with the

linear change in applied voltage at a particular frequency.

14. What is meant by active and passive elements?

If a circuit element has the capability of enhancing the energy level of a signal passing

through it is called an active element.

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




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15. What is meant by unilateral and bilateral elements?

If the magnitude of the current passing through an element is affected due to change in

the polarity of the applied voltage is called unilateral elements.

If the current magnitude remains the same even if the applied EMFs polarity is

changed is called bilateral elements.

16. What is a dual network?

In an electrical circuit itself there are pairs of terms, which can be interchanged to get

new circuits. Such pair of dual terms is given below

Current- Voltage

Open- Short

L-C

R-G

SeriesParallel

Voltage source- Current source

KCL-KVL

17. Give the steps to draw a Dual Network

In each loop of a network place a node

Draw the lines connecting adjacent nodes passing through each element and also to the

reference node.

18. Mention the disadvantages of Ohms Law.

It does not apply to all non metallic conductors

It also does not apply to non linear devices such as zener diode, vacuum tubes etc.

It is true for metal conductors at constant temperature. If the temperature changes the

law is not applicable.

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19. Compare series and parallel circuit.

S Series circuit Parallel circuit

No

1 The total effective resistance is the sum of the The reciprocal of the total effective

individual resistance ie

Reff=R1+R2+R n

resistance is the sum of the reciprocals of

individual resistance

1/Reff= 1/R1+1/R2+.1/R n

2 Only one path for the current flow More than one path for the current to

flow

3 The current flowing through all the The current flowing through each

resistances will be the same and equal to the resistance is different

total current

4 The voltage is divided across each resistance The voltage across each resistance is

according to the value of resistance. same which will be equal to the input

voltage.

20. What is a node?

A node is a point in a network in which two or more elements have a common

connection.

21. What are the classificatio

Active element

Passive element

s of Circuit elements?

Lumped and distributed elements

Bilateral and unilateral elements

Linear and non linear elements.

22. What are dependent and independent sources?

The electrical energy supplied by dependent sources a source of electrical energy.

The electrical energy supplied by independent source does not depend on another electrical

source. They convert some energy in to electrical form.

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23. Define series and parallel connection.

If the resistances are connected end to end the combination is said to be series.

24. What is a super node?

The region surrounding a voltage source which connects the two nodes directly called

super node.

25. What is principle node?

The meeting point of three or more elements is called principle node.

26. What is a closed path?

A closed path which starts at a node and travels through some part of the circuit and

arrives at the same node without crossing the node or more than once.

27. State voltage division rule.

Voltage across a resistor in series circuit is equal to the total voltage across the series

elements multiplied by the value of that resistor divided by the total resistance of the series

elements.

28. State current division rule.

The current in any branch is equal to the ratio of the opposite parallel branch

resistances to the total resistance value, multiplied by the total current in the circuit.

29. Define mesh.

A mesh is defined as a lo

30. What is a planar circuit?

p which does not contain any other loops within it.

A circuit is said to be non planar if it cannot be drawn on a plane surface without

crossovers.

31. Define super mesh.

The loop existing around a current source which is common to the two loops is called

super mesh.

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PART-B

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

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.

3. In the circuit shown, determine the current through the 2 ohm resistor and the

total current delivered by the battery. Use Kirchhoffs laws.

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

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

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

(ii) Discuss about voltage and current division principles.

(6) 6. (i) Explain :

Kirchoff laws. (4)

Dependent sources (2)

Source transformations

(2) with relevant

diagrams.

Voltage division and current division rule (4)

(ii) Calculate the resistance between the terminals AB. (4)

7. i)Determine the value of V2 such that the current through the impedance (3+j4)

ohm is zero.

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

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

9. Find the node voltages V1 and V2 and also the current supplied by the source for

the circuit shown below.

10. Find the nodal voltages in the circuit of figure.

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11. i) Using the node voltage analysis, find all the node voltages and currents in 1/3

ohm and 1/5 ohm resistances of figure.

ii) For the mesh-current analysis, explain the rules for constructing mesh impedance

matrix and solving the matrix equation [Z]I = V.

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

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

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14. Use nodal voltage method to find the voltages of nodes mand nand currents through j2 ohm andj2 ohm reactance in the networkshown below.

15. For the circuit shown find the current I flowing through 2 ohm resistance using

loop analysis.

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1. Sate superposition theorem.

UNIT II

It states that the response of a linear circuit with multiple sources is given byalgebraic sum of response due to individual sources acting alone.

2. State Thevenins theorem

It states that any linear bilateral network can be replaced by a single

VTH, in series with single impedance Zth

urrent source

3. State Nortons theorem

It states that any linear bilateral network can be replaced by a single current

source, IN in parallel with single impedance Zth.

4. State maximum power transfer theorem.

Max power is transferred to load impedance if the load impedance is the

complex conjugate of the source impedance.

5. State reciprocity theorem.

It states that in a linear, bilateral single source circuit the ratio of excitation

to the response is constant w

interchanged.

en the position of excitation and response are

6. State compensation theorem.

Let I be the current through an impedance Z in a brach of circuit.

It states that the change in current due to change in impedance in a branch

will be produced by a compensation voltage source in the same branch with

polarity opposing the original current.

7. State Millmans theorem

It states that if a number of voltage sources with internal impedance are in

parallel then they can be combined to give a voltage source with an equivalent emf and

internal impedance.

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8. State Tellegens theorem.

It states that the summation of all the product of branch voltage and its current of a

circuit is zero.

9. State the steps to solve the super position theorem.

Take only one independent voltage or current source

Obtain the branch currents

Repeat the above for

To determine the net

ther sources

ranch current just adds the currents obtained above.

10. State the steps to solve the Thevenins theorem.

Remove the load resistance and find the open circuit voltage VOC

Deactivate the consta t sources (fro voltage source remove it by internal

resistance & for current source delete the source by OC) and find the internal

resistance (RTH) of the source side looking through the open circuited load

terminals

Obtain the Thevenins equivalent circuit by connecting VOC in series with RTH

Reconnect the load resistance across the load terminals.

11. State the steps to solve the Nortons theorem.

Remove the load resistor and find the internal resistance of the source N/W

by deactivating the constant source.

Short the load terminals and find the short circuit current

Nortons equivalent circuit is drawn by keeping R TH in parallel with ISC

12. What is the Load current in a Nortons circuit?

IL= (ISC.RTH) / (RTH+RL)

13. What is the load current in Thevenins circuit?

IL= VOC / (RTH+RL)

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C TH

14. What is the maximum power in a circuit?

Max power:VO2/4 R

15. Write some applications of maximum power transfer theorem.

Power amplifiers

Communication system

Microwave transmission

16. What is the limitation of superposition theorem?

This theorem is valid only for linear systems. This theorem can be applied for

calculating the current through or voltage across in particular element. But this

superposition theorem is not applicable for calculation of the power.

17. What are the limitations of maximum power transfer theorem?

The maximum efficiency can be obtained by using this theorem is only 50% . It

is because of 50% of the power is unnecessarily wasted in Rth.

Therefore this theorem only applicable for communication circuits and not for

power circuits where efficiency is greater importance rather than power delivered.

18. State voltgae division rule.

Voltage across a resistor in a series ciruict is equal to the total voltage across

elements mulitiplied by the value of that resistor divided by the total resistance of the

series elements.

V1=(R1)*V/ (R1+R2)

19. State current division rule.

Current in any branch is equal to the ratio of the opposite paralel branch resistance to

the total resistance value, multiplied by the total current in the circuit.

I1=(R2)*I/(R1+R2)

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20. Define source transformtion.

The current and voltage sources may be inter changed without affecting the remainder

of the circuit, this technique is the source transformation. It is the tool for simplifying the

circuit.

21. List the applications of Thevinins theorem.

It is applied to all linear circuits including electronic circuits represented by the

controlled source.

This theorem is useful when t is desired to know the effect of the response in network

or varying part of the network.

22. Explain the purpose of star delta transformation.

The transformation of a given set of resistances in star to delta or vice versa

proves extremely useful in circuit analysis and the apparent complexity of a given

circuit can sometime by very much reduced.

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s equivale

PART B1. (i) 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)

ii) Determine the Thevenins 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 Thevenins equivalent across the terminals AB for the circuit shown in figurebelow. (16)

4. Find the Theveninsab.

nt circuit of the circuit shown below, to left of the terminals

Then find the current through RL = 16 ohm and 36 ohm. (16)

5. i) Find the current through branch a-b network using Thevenins theorem. (8)

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

6. i) Determine the Thevenins equivalent circuit. (8)

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

(8)

7. For the circuit shown, use sup rposition theorem to compute current I.

8. (i)Compute the current in 23 ohm resistor using super position theorem for the

circuit shown below. (8)

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(

(ii) 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.

10. i) For the circuit shown, determine the current in (2+j3) ohm by using

superposition theorem. (8)

ii) State and prove Nortons theorem. (8)

11.i) Find the value of RL so that maximum power is delivered to the

load resistance shown in figure. 8)

ii) State and prove compensation theorem. (8)

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

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13. Find the value of impedance Z so that maximum power will be transferred from source to

load for the circuit shown. (16)

14. i) State and explain maximum power transfer theorem for variable Pure resistive load.

(8) ii) Using Nortons theorem, find current through 6 ohm resistance shown in figure.

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UNIT III

RESONANCE AND COUPLED CIRCUITS

1. What is meant by Resonance?

An A.C circuit is said to be resonance if it behaves as a purely resistive circuit. The

total current drawn by the circuit is then in phase with the applied voltage, and the power

factor will then unity. Thus at resonance the equivalent complex impedance of the circuit has

no j component.

2. Write the expression for the resonant frequency of a RLC series

circuit. Resonant frequency fr=1/2LC

3. What is resonant frequency?

The frequency at which resonance occurs is called resonant frequency.

At resonant frequency XL=XC

4. Define series resonance.

A resonance occurs in RLC series circuit called series resonance. Under resonance

condition, the input current is in phase with applied voltage.

5. Define Quality factor.

The quality factor is defidissipated in one period.

ed as the ratio of maximum energy stored to the energy

6. What are half power frequencies?

In RLC circuits the frequ ncies at which the power is half the max/min power are

called half power frequencies.

7. Write the characteristics of series resonance.

At resonance impedance in min and equal to resistance therefore current is max.

Before resonant frequency the circuit behaves as capacitive circuit and above resonant

frequency the circuit will behave as inductive circuit.

At resonance the magnitude of voltage across the inductance and capacitance will be Q

times the supply voltage but they are in phase opposition.

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8. Define selectivity.

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

9. 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.

10. Write the characteristics of parallel resonance.

At resonance admittance in min and equal to conductance therefore the current is

min.

Below resonant frequency the circuits behave as inductive circuit and above

resonant frequency the circuit behaves as capacitive circuit.

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.

11. What is Bandwidth and sel ctivity?

The frequency band within the limits of lower and upper half frequency is called

bandwidth.

BW=f2-f1

Selectivity is the ratio of fr to the bandwidth

Selectivity= fr / (f2-f1)

12. What are coupled circuits?

It refers to circuit 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.

13. What are coupled circuits?

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

coupled circuits.

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14. State the properties of a series RLC circuit.

The applied voltage and the resulting current are in phase, when also means than

the p.f of RLC circuit is unity.

The net reactance isresistive part only.

zero at resonance and the impedance does not have the

The current in the circuit is max: and is V/R amperes

At resonance the circuit has got minimum impedance and max: curre t

Frequency of resonance is given by fr=1/(2LC)

15. State the properties of a parallel RLC circuit.

PF is unity

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

The value of current at resonance is minimum.

Net impedance at resonance is max: & is equal to L/RC

The admittance is min: and the net susceptance is zero at resonance.

16. Define self inductance.

When permeability is constant the self inductance of a coil is defined as the ratio of

flux linkage and current.

17. 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.

18. Define coefficient of coupling.

In coupled coils the coefficient of coupling is defined as the raction of the total flux

produced by one coil linking another coil.

19. 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.

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PART B

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

2. (i) For the circuit below, find the value of

so that current and source emf arein phase. Also find the current at this frequency. (8)

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

3. (i) A Pure resistor, a pure capacitor and a pure inductor are connected in parallel across a50Hz supply, find the impedance of the circuit as seen by the supply. Also find the resonantfrequency. (8)

(ii) 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. (i) In an RLC series circuit if 1 and 2 are two frequencies at which the magnitude of

the current is the same and if r is the resonant frequency, prove that 2 r = 12.

(ii) A series RLC circuit has Q = 75 and a pass band (between half power frequencies) of

160 Hz. Calculate the resonant

band. (8)

requency and the upper and lower frequencies of the pass

5. (i) Explain and derive the relationships for bandwidth and half power frequencies of RLC

series circuit. (8)

(ii) Determine the quality facto of a coil R = 10 ohm, L = 0.1H and C = 10f (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.

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6. What is meant by natural frequency?

If the damping is made zero then the response oscillates with natural frequency

without any opposition, such a frequency is called natural frequency of oscillations.

7. Define damping ratio.

It is the ratio orf actual resistance in the circuit to the critical resistance.

8. Write down the condition, for the response of RLC series circuit to be under damped

for step input.

The condition for the reponse of RLC series circuit to be under damped step input is

(R/2L)2>(1/LC)

9. Write down the condition fo

for step input.

the response of RLC sereis circuit to be over damped

The condition for the response of RLC series circuit to be over damped for step input

is,

(R/2L)2>(1/LC)

10. Write down the few applications of RL, RC, RLC circuits.

Coupling circuits

Phase shift circuits

Filters

Resonant circuits

AC bridge circuits

Transformers

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11. Define transient response.

The transient response is defined as the response or output of a circuit from the instant

of switching to attainment of steady state.

12. What is natural response?

The response of a circuit due to stored energy alone without external source is

called natural response or source free response.

13. What is forced response?

The response of the circuit due to the external source is called forced response.

14. Define apparent power.

The apparent power is defined as the product of magnitude of voltage and magnitude

of current.

15. What is power factor and reactive power?

The power factor is defined as the cosine of the phase difference between voltage and

current.

Power factor= cos

The reactive power of the circuit is defined as the sine of the phase angle.

Reactive power= sin

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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 lampstrike 5 sec after the switch has been closed. If R = 5Megohm, how long will it take the lamp

to strike?

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 condit ons.

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)

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6. 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.

7. 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).

8. 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

9. In the circuit shown in figure, find the current i. Assume that initial charge across the

capacitor is zero.

10. 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.

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

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UNIT V

ANALYZING THREE PHASE CIRCUITS

PART-A

1. Define line current and phase current.

The current flowing through the line is called line current

The current flowing through the phase is called phase current

2. Define line and phase voltag

The voltage between two lines is called the line voltage

The voltage between any line and the neutral point is called phase voltage.

3. Give the line and phase values in star connection

The relation between line and phase voltage in star connection is

EL=3Eph

The relation between line current and phase current in a star connection is

IL=Iph

4. Give the line and phase values in delta connection

The relation between line voltage and phase voltage in a delta connection is

EL=Eph

The relation between line current and phase current in delta connection is

IL=3Iph

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5. Write few methods available for measuring in 3-phase load.

One wattmeter method

Two wattmeter method

Three wattmeter method

6. List the methods used for power measurement with single wattmeter

Potential lead shift method

T- method

Artificial neutral method

Current transformer method

7. List the methods for unbalanced star connected load

Equivalents delta method

Mesh method

Neutral voltage displacement method

8. Write the methods of conne tions of 3 phase windings?

Independent connection

Star connection and

Delta connection

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PART B

1. With a neat circuit and phasor diagram explain the three phase power measurement by two

wattmeter methods.

2. (i) 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)

(ii) 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. (i) 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)

(ii) An alternating current is expressed as i=14.14 sin 314t. Determine rms current, frequency

and instantaneous current hen t =0.02ms. (8)

4. (i) 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)

(ii) 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. (i) Three impedances Z1 = 345 ohm, Z2 = 10 245 ohm, Z3 = 5 -90 ohm are

connected in series. Calculate applied voltage if voltage across Z1 = 27-10 V. (8)

(ii) A delta connected load as shown in figure is connected across 3 phase 100 volt supply.

Determine all line currents. (8)

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