EE 6201 – CIRCUIT THEORY SEM & BRANCH: 02& EEE+ECE

SRI ARAVINDAR
ENGINEERING COLLEGE
PONDY MAILAM ROAD, SEDARAPET P.O., VANUR

TWO & SIXTEEN MARKS

QUESTION AND ANSWERS
UNIT- 3

SUBJECT CODE : EE 6201

SUBJECT NAME : CIRCUIT THEORY

YEAR & SEM : I & II

BRANCH : ELECTRICAL & ELECTRONICS ENGG.

PREPARED BY
S. SUGANTHI,
ASSISTANT PROFESSOR – EEE

S. SUGANTHI, AP – EEE 2 & 16 Marks Q &A Page 1

EE 6201 – CIRCUIT THEORY SEM & BRANCH: 02& EEE+ECE

UNIT III

RESONANCE AND COUPLED CIRCUITS

PART A

1. Define Quality factor of a coil. (AUC May/june 2009)*

The Quality factor is the ratio of reactive power in the inductor (or) capacitor to the true
power in the resistances in series with the will or capacitor. It has no dimensions.

𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝑒𝑛𝑒𝑟𝑔𝑦 𝑠𝑡𝑜𝑟𝑒𝑑

Q= 2𝜋 × 𝑒𝑛𝑒𝑟𝑔𝑦 𝑑𝑖𝑠𝑠𝑖𝑝𝑎𝑡𝑒𝑑 𝑝𝑒𝑟 𝑐𝑦𝑐𝑙𝑒

2. 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.

3. Write the expression for the resonant frequency of a RLC series circuit.
Resonant frequency fr=1/2π√LC

4. What is resonant frequency?

The frequency at which resonance occurs is called resonant frequency. At resonant
frequency XL=XC

5. 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.

6. 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.

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EE 6201 – CIRCUIT THEORY SEM & BRANCH: 02& EEE+ECE

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.

8. 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.

9. 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.

10. What is Bandwidth and selectivity? (AU May/June 2013)*

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

BW=f2-f1

Selectivity is the ratio of resonant frequency (fr) to the bandwidth.

Selectivity= fr/ (f2-f1)

11. What are coupled circuits?

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EE 6201 – CIRCUIT THEORY SEM & BRANCH: 02& EEE+ECE

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.

12. What is single tuned and double tuned circuit?

In a coupled circuit when the capacitor is added to secondary coil to resonate the secondary,
the coupled circuit is called single tuned coupled circuit. In a coupled circuit when capacitors
are added both to primary and secondary coils to resonate the primary and secondary, the
coupled circuit is called double tuned coupled circuit.

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. (AUC May/June 2015)

Whenpermeability 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.(AUC Nov/Dec 2009)

The amount of coupling between to inductively coupled coils is expressed in terms of the
coefficient of coupling.

K=M/√L1L2

16. Write the expression for equivalent inductance of series connected magnetically coupled
coils.

For cumulative coupling effective inductance L=L1+L2+2M

For differential coupling effective inductance L=L 1+L2-2M

17. Define band width of a resonant circuit. (AU May/June 2013)

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EE 6201 – CIRCUIT THEORY SEM & BRANCH: 02& EEE+ECE

The bandwidth (BW) is defined as the frequency difference between upper cut-off frequency
(𝑓2 ) and lower cut-off frequency (𝑓1 ).

Bandwidth = 𝑓2 − 𝑓1

18. Give the applications of tuned circuits. (AU May/June 2013)

 Used in radio receivers.

 Used in communication systems.

19. Define resonant network. (AU May/June 2012)

The circuit that treat a narrow range of frequencies very differently than all other frequencies.
These are referred to as resonant circuit. The gain of a highly resonant circuit attains a sharp
maximum or minimum as its resonant frequency.

20. State ‘Dot rule’ for coupled circuits. (AU May/June 2012)

DOT Rule:

 Select a current direction in a coil 1.

 Place a dot where the current enters.
 Apply fleming’s right hand rule to the coil and find the direction of the flux.
 Apply lenz law to the second coil, the second coil flux oppose the original flux.
 Place the dot at the terminal of the second coil where the natural current leaves the
winding.

21. When do you say that a given AC circuit is at resonance? (AU April/May 2011)

 A network is in resonance when the voltage and current at the network inputterminals are
in phase.
 If inductive reactance of a network equals capacitive reactance then the network is said to
be resonance.

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EE 6201 – CIRCUIT THEORY SEM & BRANCH: 02& EEE+ECE

22. Two inductively coupled coils have self inductances L1 = 50 mH and L2 = 200 mH. If
the coefficient of coupling is 0.5, compute the value of mutual inductance between the
coils.

(AU April/May 2011)

M= K√𝐿1 𝐿2 = 0.5√50 × 200 = 50

PART B

1. A series RLC circuit shown in fig with R = 60 Ω, L= 0.5 H and C = 40 μF is connected

across an AC variable frequency and lower and upper half power frequencies. (AUC
June 2011)

2. A series RLC circuit with R=10 Ω, L= 10 mH and C=1 if it has an applied voltage of
200V at resonance frequency. Calculate the resonant frequency, the current in the
circuit and the voltage across the elements at resonance. Find also the quality factor
and bandwidth for the circuit.(AUC June 2011)

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EE 6201 – CIRCUIT THEORY SEM & BRANCH: 02& EEE+ECE

3. Derive the expression for the half power bandwidth of the parallel resonant circuit.

4. Derive the mutual inductance and magnetic coupling coefficient (K) of the transformer
with neat illustration. (AUC May/June 2015)

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EE 6201 – CIRCUIT THEORY SEM & BRANCH: 02& EEE+ECE

5. Derive the expressions for equivalent inductance of two coils in series and parallel with

a) Series aiding

b) Series opposition

c) Parallel aiding

d) Parallel opposition (AUC June 2011)

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EE 6201 – CIRCUIT THEORY SEM & BRANCH: 02& EEE+ECE

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