Self Inductance by Rayleigh's Method

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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.

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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

Time for 10 oscillation s 78.26 79.33 78.52 77.63 78.21

Time period Mean T T¯ s s 7.826 7.933 7.852 7.839±6.19 × 10−2 7.763 7.821

Calculation : Using equation (6) we get the inductance to be, L1 L2 L3 L4 L5

= 0.8378 H = 0.8842 H = 0.8297 H = 0.8522 H = 0.8505 H ¯ = (0.85088 ±.0208) H Average inductance L

Differentiating eq. (6) with x y and T we can calculate the uncertainity of this result, ∂L =0.1061 ∂T

H/s=0.1061 Ω

∂L =0.29732 ∂x ∂L =0.1698 ∂y

H H

σL =0.0917 H

Result : ¯ = (0.85088 ±.0917) H L Percentage of error is 6.3% as the standard value is 0.8 H.

Discussion : Human error in counting the distance of deflection adds to errors. This could be improved by taking more data. The scale we used was hand made and may not be properly leveled. In such case, the coil will not oscillate in a vertical plane and will lead to incorrect observations,this unacuracy in calibration leads some error.If the spot of light is not properly adjusted on the zero of the scale, all the observations for n as well as for the C.D.R. are liable to be incorrect, so we take this with much care. And he plugs of the resistance boxes may not be clean, or may be loose due to which the 4

actual value of the resistance introduced in the circuit may be different from what is observed. In the measurement of the distance (d) between the two consecutive deflection follow a constant proportion. Basically there is a better way to measure the inductance with the help of a capacitor (Anderson’s method) which leads us to a more sensitive approach to measure inductance.

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