Experiment 3 APPLIED PHYSICS

EQUIVALENT INDUCTANCE IN SERIES AND PARALLEL COPULING; COUPLING COEFFICIENT

3.1 OBJECTIVES:

1. Measure equivalent inductance of two coils, for series coupling with aiding current and opposing current.

2. Measure equivalent inductance of two coils, for parallel coupling with aiding current and opposing current

3. Determine Coupling Coefficient ‘k’ as a function of distance and plot it.

3.2 SAFETY NOTES:

1. Power off LCR meter while making connections and after performing the lab.2. Carefully handle the apparatus. Do not drop the helmholtz coils or LCR meter down

while performing the experiment.3. Make connections carefully and call teacher to check the connections before starting

the experiment.

3.3 EQUIPMENTS/ REQUIREMENTS:

1. A Pair of coils.2. LCR meter3. 1 meter scale.4. 4 connecting leads with banana connectors

3.4 THEORY:

Inductance:According to Farraday’s law, “The induced emf in a circuit is equal to the negative of the rate at which the magnetic flux through the circuit is changing with time.”

(1)

It is an ability of a conductor to induce voltage when the current changes. the smbol for inductance is L and its unit is henry (H).

(2)

Mutual Induction:When the current in a inductor changes, the varying flux can cut across an other inductor nearby, producing induced voltage in both inductors. This is called Mutual induction. The unit of mutual inductance is also henry (H).Coefficient of Coupling:The fraction of total flux from one coil linking another coil is the coefficient of coupling ‘k’ between the coils.

(3)

If k <1 then there is loose coupling between the coils if k has high value than there is tight coupling between them and if k=0 then there is no mutual inductance. In terms of mutual inductance.

Lab Instructor Arshia Aijaz P a g e | 3 – 1

Experiment 3 APPLIED PHYSICS

Inductances in Series:When two coils are joined in series then the equivalent inductance is influenced by their mutual coupling as well as direction of current in the coils.If current in the coils are in same direction (aiding current) then their flux are additive i.e. in same direction. So the equivalent inductance increases.

La= L1 + L2 +2M (5)

If current in the coils are in opposing direction (opposing current) then some amount of their flux cancel each other. So the equivalent inductance decreases.

Lo= L1 + L2 -2M (6)

Using equation 5 and 6 average mutual inductance is fount to be M=( La - Lo)/4 (7)

Inductances in Parallel:If current in the coils are in same direction (aiding current) then their flux are additive i.e. in same direction. So the equivalent inductance becomes

(8)

If current in the coils are in opposite direction (opposing current) then their equivalent inductance becomes

(9)

3.5 REFERENCES:

1. ‘Basic Electronics’, GROB2. ‘Physics’ by Halliday Resnick and Krane.3. ‘A text book of Electrical Technology’ by B.L.Theraja, A.K.Theraja

3.6 EXPERIMENTAL SETUP:

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Experiment 3 APPLIED PHYSICS

3.7 PROCEDURE:1. Measure the inductance L1 and L2 of both coils.2. Make connections for series coupling with aiding current as shown in figure 1.3. Vary distance between coils from 5cm to 15cm through a step of 1cm and measure

inductance each time.4. Repeat the above procedure for series coupling with opposing current and parallel

coupling with aiding and opposing current.

3.8 OBSERVATIONS: L1 = ________mH, L2 = __________mH

For Series:

Distance 'x'cm

Inductance (mH) Mutual Inductance

m(H)

Coupling Coefficient

'k'aiding current

opposing current

                                             

For Parallel:

Distance 'x'cm

Inductance (mH) Mutual Inductance

m(H)

Coupling Coefficient

'k'aiding current

opposing current

                                             

3.9 GRAPH:

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Experiment 3 APPLIED PHYSICS

Plot graph between coupling coefficient ‘k’ versus distance ‘x’ using your observations.

3.10 RESULT AND DISCUSSION:

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