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PHYSICS INVESTIGATORY PROJECT

Study of the Factors Affecting the Self-Inductance of a Coil

Certificate

Index

S.NO CONTENTS

1. Aim,

2. Apparatus,

3. Introduction,

4. Theory,

5. Procedure,

6. Observation

7. Result,

Aim

To study the factor on which the self inductance of a coil depends

by observing the effect of this coil, when put in series with a

resistor (bulb) in a circuit fed up by an A.C.source of adjustable

frequency.

Apparatus

A coil of large turns, a.c. source of adjustable frequency, an

electrical bulb,(6v) a.c. ammeter of suitable range rheostat, a doft

iron rod, one way key , connecting wires etc

Theory

Self inductance is the property of a coil which opposes the change in current through it.

The self inductance of a coil (long solenoid) is

where μr = Relative magnetic permeability of magnetic material,

N = Total number of turns in solenoid

A = Area of cross-section of solenoid

l = length of solenoid.

Hence, the self inductance depends upon:

1. No. of turns (N), L α N

2. Geometry of coil, L α A, L α 1/l

3. Nature of core material, L α μ

When an inductor is connected in series with a resistor (bulb) with a variable source of frequency, then current flowing in the bulb is

Where Z = √R2 + ω2L2 = Impedance of the a.c. circuit. Here

R = Resistance of the bulb

L = Self inductance of coil

ω = 2πf = Angular frequency of a.c. source.

The brightness of bulb i.e., Heat generated in the bulb is

CIRCUIT DIAGRAM:

Factors Affecting Self-Inductance

1. Number of turns: L ∝ N²
2. Area of cross-section: L ∝ A
3. Length of coil: L ∝ 1/l
4. Core material: L ∝ μr Increasing turns, area or permeability increases inductance, whereas increasing length decreases inductance.

Procedure

1. Make all connections as shown in the circuit diagram.

2. Switch on the a.c. supply & adjust the current in the circuit by using the

variable

resistor ( Rh ).

3. Record the current in a.c. ammeter & see the brightness of bulb.

4. Now, put the soft iron rod inside the conductor core & record the current

in a.c. ammeter & again check the brightness of bulb. The current &

brightness both decreases.

5. Now, switch off the supply & decrease the frequency of a.c. source (say

50 Hz).

6. Again switch on the supply & adjust the current in circuit at same

constant voltage 6V

by using the rheostat. Note the current in ammeter & brightness of bulb. The

current &

brightness both will increase.

7. Again insert the iron rod in the core of coil & note the current &

brightness. The current

& brightness both decreases.

8. Repeat the steps 5, 6 and 7 for different

frequency of a.c. source.

Calculations For L = 0.5 H and f = 50 Hz, XL = 2πfL = 157 Ω. For f = 100 Hz, XL = 314 Ω. Hence reactance doubles when frequency doubles.

Result

1. The current in the circuit decrease on inserting the iron rod in the core of coil at

constant frequency of applied voltage & brightness of bulb decreases & vice-versa.

2. The current in the circuit increases on decreasing the frequency of applied voltage

& vice-versa. Therefore, the brightness of bulb increases.

Sources of Error

Heating of coil, fluctuations in voltage, observational error

in brightness estimation, imperfect core placement and

instrument inaccuracies.

1. The resistance of circuit may increase slightly due to

heating effect of current.

2. There may be eddy current in soft iron coil.

Conclusion The experiment verifies the dependence of self-inductance on physical and material properties of a coil and demonstrates the role of inductive reactance in AC circuits.