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LAKSHMI NARAIN COLLEGE OF TECHNOLOGY, INDORE ELECTRICAL AND ELECTRONICS DEPARTMENT

Electrical and Electronics Lab. Lab Manual

Date

:

Experiment No.

:

Date of Conduction

:

Date of Submission

:

OBJECT

:Measurement of R,L,C &Q using LCR Q Meter

Apparatus:- LCR Q Bridge Kit, Resistance, Capacitor and Inductor, Two Patch chords whose one side is banana plugged and other side is crocodile clip. Q meter:- Every coil has effective resistance whose behavior is different for different frequencies and arises because of eddy current , skin effect etc. this is different from DC resistance. It should be of low value otherwise coil have more power loss (I2R). The ratio of inductive reactance to effective resistance is known as Q factor or Quality Factor, or magnification factor. Q =ω L Reff Q- Meter is an instrument which measures the value of quality factor (Q) directly. Capacitor and inductor are energy storing devices for which quality factor is defined as Q = 2п X maximum energy stored per cycle energy dissipated per cycle = ω0L R

Where ω0 is the resonant frequency, L is the inductance and R is the effective resistance of the coil. The effective resistance, R , is never determined directly. Its value depends upon the value of the frequenc. The value of the effective resistance with AC differs from its DC value due to skin effect and eddy current loss.since the value varies in a complex manner with frequenc, it is directly determined by measuring the value of Q. Q-Meter Measurement:- There are three methods of making measurement dependent upon the size of the components. 1.Direct Connection Method:- It is used for medium Q coils.Select a frequency on the oscillator. Current limiting resistor is adjustable to fed selected amount of current to the insertion resistor which is of small value of .02Ω. This resistor acts as a voltage source which is shown as multiplying Q by meter. Connect the unknown resonant circuit by varying the oscillator frequency or by varying the capacitor condition .Resonance is indicated by Q voltmeter. Procedure:1. Note the value of C,Vc,V 2. Q is calculated as Q = Vc Ve 3. L can be estimated using three relations f=1 2п√LC 2 f = 1 4п2LC L= = 1 4п2FC Assumptions:1. Internal impedence of voltage source is neglected. 2. The capacitor is assumed to be non leaky. 3. Inverting capacitance is neglected. Result:- Measured Q is less than actual Q.

Series Connection Method:- It is used for low Q coil Procedure:1. 2. 3. 4. 5.

Connect the unknown Zwith work coil. Short circuit Z with the switch. Resonate the circuit and note down C1 and Q1 Remove the short circuit Resonate the circuit and note down C2 and Q2

During first reading 1 ωc1

Xc = XL ω

= WL ω

Q1 = 1 ωc1Rω

= ωL ω ……..........(1) Rω

During Second reading

Xc2 = XL ω +Xc

Xs =reactance of unknown which appears in series with work coil. Xs = Xc2 - XL ω =Xc2-Xc1 = 1 - 1 ωc2 ωc1

from 1

Xs =C1-C2 ωCC2 If unknown is inductor

Xs = ωLS,

C1>C2

ωLS = C1C2 ω C1C2 Ls = C1-C2 ω2 C1C2 If unknown is capacitor Xs =

1 ω C1

,

C1>C2

1 ω Cs

= C2-C1 ω C2C2

Cs = C1C2 C2-C1 Eqn (2)

Q1 = 1 ωC1Rω Rω = 1 ωC1Q1 Q2 = 1 ωC2Q2

Unknown resistor Rs= R2-Rω =1 ωC2Q2

1 ωC1Q1

Parallel Connection Method:- It is used for high Q coils Procedure:1. Resonate the circuit without connecting unknown coil note down C1,Q1. 2. Connect the unknown coil and resonate the circuit. During first reading

Xc = XL ω 1 ωc1

= WL ω

Q1 = 1 ωc1Rω

= ωL ω ……..........(1) Rω

During Second reading = Xc2ǁǁ Xp = XLω Xc2 Xp =XLω =Xc1 Xc2+ Xp

During Second reading XczXp =XC1Xc2+ XC1Xp Xp(Xc2-Xc1) =Xc1 Xc2 Xp= Xc1 Xc2 Xc2- Xc1 1 ωc1

.1 ωc2

1 ωc2

-1 ωc1

Xp= ωc1-ωc2 ωc1-C2 Xp = 1 ωc1-C2 Observation Table S.no

Inductance L (mH) at 100 Hz

at 1 kHz

Resistance R (Ω) at 100 Hz

at 1 kHz

Q-Factor ω/R measured at 100 Hz

Result. The value of Q increases with frequency Q meter =

at 1 kHz at 100 Hz

Q calculated

at (1kHz) at (100Hz) ******

at 1 kHz

Q-Factor observed at 100 Hz

at 1 kHz

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Electrical and Electronics Lab. Lab Manual

Date

:

Experiment No.

:

Date of Conduction

:

Date of Submission

:

OBJECT

:Measurement of R,L,C &Q using LCR Q Meter

Apparatus:- LCR Q Bridge Kit, Resistance, Capacitor and Inductor, Two Patch chords whose one side is banana plugged and other side is crocodile clip. Q meter:- Every coil has effective resistance whose behavior is different for different frequencies and arises because of eddy current , skin effect etc. this is different from DC resistance. It should be of low value otherwise coil have more power loss (I2R). The ratio of inductive reactance to effective resistance is known as Q factor or Quality Factor, or magnification factor. Q =ω L Reff Q- Meter is an instrument which measures the value of quality factor (Q) directly. Capacitor and inductor are energy storing devices for which quality factor is defined as Q = 2п X maximum energy stored per cycle energy dissipated per cycle = ω0L R

Where ω0 is the resonant frequency, L is the inductance and R is the effective resistance of the coil. The effective resistance, R , is never determined directly. Its value depends upon the value of the frequenc. The value of the effective resistance with AC differs from its DC value due to skin effect and eddy current loss.since the value varies in a complex manner with frequenc, it is directly determined by measuring the value of Q. Q-Meter Measurement:- There are three methods of making measurement dependent upon the size of the components. 1.Direct Connection Method:- It is used for medium Q coils.Select a frequency on the oscillator. Current limiting resistor is adjustable to fed selected amount of current to the insertion resistor which is of small value of .02Ω. This resistor acts as a voltage source which is shown as multiplying Q by meter. Connect the unknown resonant circuit by varying the oscillator frequency or by varying the capacitor condition .Resonance is indicated by Q voltmeter. Procedure:1. Note the value of C,Vc,V 2. Q is calculated as Q = Vc Ve 3. L can be estimated using three relations f=1 2п√LC 2 f = 1 4п2LC L= = 1 4п2FC Assumptions:1. Internal impedence of voltage source is neglected. 2. The capacitor is assumed to be non leaky. 3. Inverting capacitance is neglected. Result:- Measured Q is less than actual Q.

Series Connection Method:- It is used for low Q coil Procedure:1. 2. 3. 4. 5.

Connect the unknown Zwith work coil. Short circuit Z with the switch. Resonate the circuit and note down C1 and Q1 Remove the short circuit Resonate the circuit and note down C2 and Q2

During first reading 1 ωc1

Xc = XL ω

= WL ω

Q1 = 1 ωc1Rω

= ωL ω ……..........(1) Rω

During Second reading

Xc2 = XL ω +Xc

Xs =reactance of unknown which appears in series with work coil. Xs = Xc2 - XL ω =Xc2-Xc1 = 1 - 1 ωc2 ωc1

from 1

Xs =C1-C2 ωCC2 If unknown is inductor

Xs = ωLS,

C1>C2

ωLS = C1C2 ω C1C2 Ls = C1-C2 ω2 C1C2 If unknown is capacitor Xs =

1 ω C1

,

C1>C2

1 ω Cs

= C2-C1 ω C2C2

Cs = C1C2 C2-C1 Eqn (2)

Q1 = 1 ωC1Rω Rω = 1 ωC1Q1 Q2 = 1 ωC2Q2

Unknown resistor Rs= R2-Rω =1 ωC2Q2

1 ωC1Q1

Parallel Connection Method:- It is used for high Q coils Procedure:1. Resonate the circuit without connecting unknown coil note down C1,Q1. 2. Connect the unknown coil and resonate the circuit. During first reading

Xc = XL ω 1 ωc1

= WL ω

Q1 = 1 ωc1Rω

= ωL ω ……..........(1) Rω

During Second reading = Xc2ǁǁ Xp = XLω Xc2 Xp =XLω =Xc1 Xc2+ Xp

During Second reading XczXp =XC1Xc2+ XC1Xp Xp(Xc2-Xc1) =Xc1 Xc2 Xp= Xc1 Xc2 Xc2- Xc1 1 ωc1

.1 ωc2

1 ωc2

-1 ωc1

Xp= ωc1-ωc2 ωc1-C2 Xp = 1 ωc1-C2 Observation Table S.no

Inductance L (mH) at 100 Hz

at 1 kHz

Resistance R (Ω) at 100 Hz

at 1 kHz

Q-Factor ω/R measured at 100 Hz

Result. The value of Q increases with frequency Q meter =

at 1 kHz at 100 Hz

Q calculated

at (1kHz) at (100Hz) ******

at 1 kHz

Q-Factor observed at 100 Hz

at 1 kHz

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