Determination of self-inductance of a coil by Anderson's method
.
Experiment :B-03
Determination of self inductance of a coil by Rayleigh’s method. Submitted by
Muhammed Mehedi Hassan
Group A ;Batch-09
Second Year, Roll–SH 236
Student of Physics Department,
Uinversity of Dhaka.
Date of experiment September 27, 2011.
Date of submission October 30 , 2011.
1
Experiment :B-03
Determination of self inductance of a coil by Rayleigh’s method.
Theory :
Figure 1: Rayleigh’s method circuit diagram.
If a potential V applied to a condenser of capacitance C, imparts Q units of charge to the condenser then,
Q
V
From the ballistic galvanometer working formula we got:
C=
T i θ1 θλ (1 + ) πθ 2
2
T i θ1 θ1
Q=
π θs 2 θ3
Where, θs = the maximum displacement of the steady deflection,
T=period of the oscillation, λ=logaritmmic decrement of the galvanometer coil.
We know that,
Q = nLio
Q=
(1)
(2)
(3)
(4)
Therefore , from equation (3) and (4) we can write,
L=
Replacing x =
θ1 θs and y 4 =
T r θ1 θ1 1
( )( ) 4 π 2 θs θ3
(5)
θ1 θ3 Tr xy π2
From this equation the absolute capacitor of a condenser can be found.
L=
2
(6)
Apparatus :
1. An inductor (inductance to be measured)
2. A ballistic galvanometer with light scale arrangement
3. A shunt box
4. A high resistance box
5. A cell
6. Key (taping and morse key) and
7. lamp
Table -1:Determination of θ1 and θ3 hence obtain x and y :
No.
Ratio of
of
P
Q
obs.
1
2
3
4
5
Displacement of ballistic galvanometer mm
Make
Break
Mean
θ1
Steady deflection θs
θ1
θ3
θ1
θ3
30
1/1
31
30
44
10/10
45
44
52
100/100
53
52
70
1000/1000 72
73
91
10000/10000 90
92
20
21
22
39
40
39
42
43
43
57
58
58
74
73
74
30
31
30
45
44
44
53
53
54
71
72
72
91
92
91
21
21 30.33
20.5
20 ±0.577 ±0.577
39
40 44.33
39.33
39 ±0.577 ±0.577
43
42 53.17
42.5
42 ±0.577 ±0.577
58
59 71.67
57.83
57 ±1.0
±1.0
73
72 91.16
73.83
74 ±1.0
±1.0
3
θ3
x
y
mm
10
3.033 1.107
16
2.770 1.127
20
2.658 1.251
26
2.766 1.239
33
2.762 1.234
Table -2:Determination of the time period T :
No.
of observation 1
2
3
4
5
Experiment :B-03
Determination of self inductance of a coil by Rayleigh’s method. Submitted by
Muhammed Mehedi Hassan
Group A ;Batch-09
Second Year, Roll–SH 236
Student of Physics Department,
Uinversity of Dhaka.
Date of experiment September 27, 2011.
Date of submission October 30 , 2011.
1
Experiment :B-03
Determination of self inductance of a coil by Rayleigh’s method.
Theory :
Figure 1: Rayleigh’s method circuit diagram.
If a potential V applied to a condenser of capacitance C, imparts Q units of charge to the condenser then,
Q
V
From the ballistic galvanometer working formula we got:
C=
T i θ1 θλ (1 + ) πθ 2
2
T i θ1 θ1
Q=
π θs 2 θ3
Where, θs = the maximum displacement of the steady deflection,
T=period of the oscillation, λ=logaritmmic decrement of the galvanometer coil.
We know that,
Q = nLio
Q=
(1)
(2)
(3)
(4)
Therefore , from equation (3) and (4) we can write,
L=
Replacing x =
θ1 θs and y 4 =
T r θ1 θ1 1
( )( ) 4 π 2 θs θ3
(5)
θ1 θ3 Tr xy π2
From this equation the absolute capacitor of a condenser can be found.
L=
2
(6)
Apparatus :
1. An inductor (inductance to be measured)
2. A ballistic galvanometer with light scale arrangement
3. A shunt box
4. A high resistance box
5. A cell
6. Key (taping and morse key) and
7. lamp
Table -1:Determination of θ1 and θ3 hence obtain x and y :
No.
Ratio of
of
P
Q
obs.
1
2
3
4
5
Displacement of ballistic galvanometer mm
Make
Break
Mean
θ1
Steady deflection θs
θ1
θ3
θ1
θ3
30
1/1
31
30
44
10/10
45
44
52
100/100
53
52
70
1000/1000 72
73
91
10000/10000 90
92
20
21
22
39
40
39
42
43
43
57
58
58
74
73
74
30
31
30
45
44
44
53
53
54
71
72
72
91
92
91
21
21 30.33
20.5
20 ±0.577 ±0.577
39
40 44.33
39.33
39 ±0.577 ±0.577
43
42 53.17
42.5
42 ±0.577 ±0.577
58
59 71.67
57.83
57 ±1.0
±1.0
73
72 91.16
73.83
74 ±1.0
±1.0
3
θ3
x
y
mm
10
3.033 1.107
16
2.770 1.127
20
2.658 1.251
26
2.766 1.239
33
2.762 1.234
Table -2:Determination of the time period T :
No.
of observation 1
2
3
4
5