Chettinad College of Engineering and Technology-Karur

CHETTINAD COLLEGE OF ENGINEERING AND TECHNOLOGY-KARUR

DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING

I YEAR / II SEM

UNIT III-RESONANCE AND COUPLED CIRCUITS

2 MARKS

1.Define bandwidth:-

The difference between power frequencies f1 and f2 at which power is half of its maximum is called bandwidth. It’s denoted as, b.

B.W= F1 – F2

2.Define selectivity.

The selectivity is defined as the ratio of the bandwidth to the resonant frequency.

Selectivity = b / fr

3.Define Quality factor. APR’05, Nov’ 03

It is defined as the ratio of wr to bandwidth and it is expressed as

Q= wr / B.W

4.Write down the significance of quality factor.

1.It indicates the selectivity or sharpness of the tuning of a series circuit.

2.These circuits used in radio circuits.

5.Write down the expression for lower and upper cut off frequencies.

F1 = fr - Df

F2 = fr + Df

6.Draw the parallel circuit used for the parallel resonance. NOV’05

7.Write down the expression for resonant frequency:-

fr = 1 / 2ÕÖLC

L- inductance in H

c-capacitance in farad

8.Write down the formula used to calculate quality factor of the parallel resonance:-

The parallel circuit used to magnify the current and hence known as current resonance circuit. Q= I/ R(ÖL/C)

9. What are coupled circuits?

The two circuits are said to be coupled circuits if all or part of the electrical energy supplied to one circuit is transferred to the other circuit, without having any electrical connection between them.

10.Give some examples of coupled circuits:-

· Transformer, Gyrator.

11.What are magnetically coupled circuits?

When the two circuits are placed very close to each other such that a magnetic flux produced by one circuits links with both the circuits, then the two circuits are said to be MAGNETIC CIRCUITS.

12.Define mutually coupled coils:-

When two or more coils are placed very close to each other, then the current in one coil affects other coils by inducing voltage in them, such coils are called as mutually coupled coils.

13.Define self-induction.

According to Faraday’s Law, due to the rate of change of flux linkages, there will be induced e.m.f in the coil. The Phenomenon is called self induction.

14.When will the self-inductance in a coil dies?

SELF INDUCTANCE lasts in a coil till the current changes in a coil.

15.What is self-inductance?

The property of the coil, which opposes any changes in the current passing through it, is called SELF INDUCTANCE.

16.Define co-efficient of self-inductance:-

The co-efficient of self-inductance is defined as the flux linkages per ampere current in it. Its unit is Henry (H).

17.Define Mutually induced e.m.f.:-

If the flux produced by one coil links with the other coil, placed sufficiently close to the first coil, then due to the change in the flux produced by first coil, there is induced e.m.f in the second coil. Such induced e.m.f in the second coil is called MUTUALLY INDUCED E.M.F.

18.Define Mutual inductance:- May’06

The co-efficient of mutual inductance is the property by which e.m.f gets induced in a coil because of change in current in other coil. It is also called Mutual Inductance. Its unit is Henry.

19.Define the co-efficient of coupling:- Nov’04,Nov’05, Apr’04

The CO-EFFICIENT OF COUPLING gives the idea about the magnetic coupling between the two coils. The maximum value of K is unity.

20.State the value of K for the coupled coils:-

K = M

ÖL1L2

When K = 1, the coupling coils are Tightly or Perfectly coupled coils.

K < 1, the coupling coils are Loosely coupled coils.

21.Interpret the Dot conventions. Nov’05

· If the current enters a dot in one coil, then mutually induced voltage in other coil is positive at the dotted end.

· If the current leaves a dot in one coil, then mutually induced voltage in other coil is negative at the dotted end.

22.State the condition for resonance in RLC series circuit:-May’06

In series RLC circuit, series resonance occurs when inductive reactance XL = Capacitive reactance XC

23.What do you understand by series resonance and parallel resonance? Nov’04

Series resonance

A Series RLC circuit is said to be in resonance3 if the current is in phase with the applied voltage.

Parallel resonance

A Parallel RLC circuit is said to be in resonance3 if the current is in phase with the applied voltage.

24. Define Mutual induction:- Nov’03

25.Express resonant frequency interms of half power frequencies:-Dec’05

The resonant frequency is given by the geometric mean of the two half power frequencies.

fr = Öfhfl

26.What is resonance:-

It’s a circuit condition at which a RLC circuit behave as purely resistive circuit.

27.Determine the resonant frequency for the circuit:- May’04

R =10ohm; L = 0.5mH ; C = 10mF

Angular frequency of resonance, wr = 1 / Ö LC

= 1 / Ö 0.5(10 )10(10 )

Resonanat Frequency, fr = wr / 2Õ.

28. What do you understand by parallel resonance? Nov’04

Parallel resonance

A Parallel RLC circuit is said to be in resonance3 if the current is in phase with the applied voltage.

DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING

I YEAR / II SEM

UNIT III-RESONANCE AND COUPLED CIRCUITS

12 MARKS:

1.Explain in brief the concept of self-inductance and mutual inductance.

Reference book & Page no: Sudhakar shyam mohan– 402

2.Explain with neat diagram dot conversion:-

Reference book & Page no: Sudhakar shyam mohan– 404

3.Derive the expressions for equivalent inductance of two coils in series with

i) Series aiding ii) series opposition.

Reference book & Page no: Sudhakar shyam mohan– 417

4.Derive the expressions for equivalent inductance of two coils in series with

i) Parallel aiding ii) parallel opposition.

Reference book & Page no: Sudhakar shyam mohan– 418

5.In the parallel RLC circuit, calculate resonant frequency, bandwidth, Q factor and power dissipated at half power frequencies. May’06

6.Calculate the phasor currents I1 and I2 in the circuit. May’06

7.Determine the equivalent impedance. Nov’04

8.Determine the total impedance, current, phase angle and the voltage across each element. Nov’04

9.A coil of resistance 10 ohm and inductance 0.5 H is connected in series with a capacitor. On applying sinusoidal voltage, the current is maximum when frequency is 50 Hz. A second capacitor is connected in parallel with this circuit: what capacitance must it have so that the combination acts like a non inductive resistor at 100 Hz? Calculate the total current supplied in each case if the applied voltage is 220V. Nov 03

10.The combined inductance of two coils connected in series is 0.6 H or 0.1 H, depending on the relative directions of the currents in the coils. If one of the coils when isolated has a self-inductance of 0.2 H, calculate the mutual inductance and the coefficient of coupling. Nov’03

11.Two resistors R1 = 2500 ohm and R2 are joined in series and connected to a 100 v supply. The voltage drops across R1 and R2 are measured successively by a voltmeter having a resistance of 50000 ohm. Find the sum of the two readings. Nov’03

12.A series RLC circuit consists of R=100 ohm, L=0.02 H and C=0.02 m F.Calculate frequency of resonance. A variable frequency sinusoidal voltage of constant RMS value of 50 V is applied to the circuit. Find the frequency at which voltage across L and C is maximum. Also calculate the voltages across L and C is maximum. Also calculate voltages across L and C at frequency of resonance. Find maximum current in the circuit. Nov’05

13.A series RLC circuit consists of 50 ohm resistance 0.2 H inductance and 10 m F capacitance with the applied voltage of 20 V. Determine the resonant frequency. Find the Q factor of the circuit. Compute the lower and upper frequency limits and also find the bandwidth of the circuit. Apr’04

14.Derive an expression for current response of RLC series circuit with sinusoidal excitation. Assume the circuit is working in critical damping. Nov’05

15.A 100 ohm resistor and a 20 mH inductor are connected in series across a 230 V, 50 Hz supply. Find circuit impedance, admittance, current , voltage a/c resistance, voltage a/c inductor, apparent power, active power and power factor. Nov’05

16.A series RLC circuit has R=20 ohm, L= 0.005 H and C=0.2 X 10 – 6 F. It is fed from a 100 V variable frequency source. Find i. Frequency at which current is maximum ii. Impedance at this frequency and iii. Voltage a/c inductance at this frequency. Nov’05

DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING

I YEAR / II SEM

UNIT III-RESONANCE AND COUPLED CIRCUITS

GLOSSARY

Ø Self Inductance

An electric current i flowing around a circuit produces a magnetic field and hence a magnetic flux Φ through the circuit. The ratio of the magnetic flux to the current is called the inductance, or more accurately self-inductance of the circuit.

Ø Mutual inductance

Mutual inductance is the concept that the change in current in one inductor can induce a voltage in another nearby inductor. It is important as the mechanism by which transformers work, but it can also cause unwanted coupling between conductors in a circuit.

Ø Coefficient of coupling

The coefficient of coupling is always between 1 and 0, and is a convenient way to specify the relationship between a certain orientation of inductor with arbitrary inductance:

Where

k is the coefficient of coupling and 0 ≤ k ≤ 1,

L1 is the inductance of the first coil, and

L2 is the inductance of the second coil.

Ø RLC Circuit

An RLC circuit (also known as a resonant circuit or a tuned circuit) is an electrical circuit consisting of a resistor (R), an inductor (L), and a capacitor (C), connected in series or in parallel.

Ø Quality Factor

The quality factor of a parallel resonance circuit is defined as the ratio of the magnitude of the inductor/capacitor susceptance and the conductance.

Ø Frequency Response of a Series –Resonant circuit

Ø Usefulness of 'Q'

The Q factor is particularly useful in determining the qualitative behavior of a system.

For example, a system with Q less than or equal to 1/2 cannot be described as oscillating at all, instead the system is said to be in an overdamped (Q < 1/2) or critically damped (Q = 1/2) state.

However, if Q > 1/2, the system's amplitude oscillates, while simultaneously decaying exponentially. This regime is referred to as underdamped.

Ø Bandwidth

It is the difference between the upper and lower cutoff frequencies.

Ø Frequency Response of a Parallel –Resonant circuit