Electrical lab manual

VERIFICATION OF KIRCHOFF’S VOLTAGE LAW

AIM:

       To verify Kirchoff’s voltage law for the given circuit.

APPARATUS REQUIRED:

S.No	Components	Specification	Quantity
1	Resistor	1k,2.2k,3.3k	1
4	Voltmeter	(0-30)V	3
5	Bread Board		1
6	Regulated Power Supply	0-30V	1

THEORY:

Kirchoff’s voltage law is based on the principle of conservation of energy.  This  requires that the total work done in taking a unit positive charge around a closed path and ending up at the original point is zero. This gives us our basic Kirchoff’s law as the algebraic sum of the potential differences taken round a closed loop is zero.  

i.e.  around a loop,  Σ Vr = 0,      

where  Vr  are the voltages across the branches in the loop.

 

va + vb + vc + vd – ve = 0

This is also sometimes stated as the sum of the emfs taken around a closed loop is equal to the sum of the voltage drops around the loop. Although all circuits could besolved using only Ohm’s Law and Kirchoff’s laws, the calculations would be tedious.  Various network theorems have been formulated to simplify these calculations.

PROCEDURE:

1.      Connect the circuit as per the circuit diagram.

2.      Vary the input voltage and measure the voltage across each voltmeter.

3.      Verify the theoretical value with practical value.

RESULT:

              Thus the Kirchoff’s voltage law is verified for the given circuit.

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VERIFICATION OF KIRCHOFF’S CURRENT LAW

AIM:

       To verify Kirchoff’s current law for the given circuit.

APPARATUS REQUIRED:

S.No	Components	Specification	Quantity
1	Resistor	1k,2.2k,3.3k	1
4	Ammeter	(0-30)mA	3
5	Bread Board		1
6	Regulated Power Supply	0-30V	1

THEORY:

Kirchoff’s current law is based on the principle of conservation of charge.  This  requires that the algebraic sum of the charges within a system cannot change.  Thus the total rate of change of charge must add up to zero.  Rate of change of charge is current. This gives us our basic Kirchoff’s current law as the algebraic sum of the currents meeting at a point is zero. i.e.  at a node,  Σ Ir = 0,  where  Ir  are the currents in the branches meeting at the node This is also sometimes stated as the sum of the currents entering a node is equal to the sum of the current leaving the node. The theorem is applicable not only to a node, but to a closed system.

i1 + i2 – i3 + i4 – i5 = 0

i1 + i2 + i4  =  i3 + i5

PROCEDURE:

1.      Connect the circuit as per the circuit diagram.

2.      Vary the input voltage and measure the current through each Ammeter reading.

3.      Verify the theoretical value with practical value.

RESULT:

              Thus the Kirchoff’s current law is verified for the given circuit.

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VERIFICATION OF SUPERPOSITION THEOREM

AIM:

          To verify the superposition theorem for the given circuit.

APPARATUS REQUIRED:

S.No	Components	Specification	Quantity
1	Resistor	1k,2.2k,3.3k	1
4	Ammeter	(0-30)mA	3
5	Voltmeter	(0-30)V	2
5	Bread Board		1
6	Regulated Power Supply	0-30V	1

THEORY:

The superposition theorem tells us that if a network comprises of more than one source, the resulting currents and voltages in the network can be determined by taking each source independently and superposing the results.

If  an excitation  e1(t) alone gives a response r1(t), 

and an excitation  e2(t)  alone gives a response r2(t),

then, by superposition theorem, if the excitation  e1(t) and the excitation  e2(t) together would

give a response  r(t) = r1(t) + r2(t)

The superposition theorem can even be stated in a more general manner, where the

superposition occurs with scaling.

Thus an excitation of   k1 e1(t) and an excitation of   k2 e2(t) occuring together would give a

response of  k r (t) + k  r (t).

PROCEDURE:

1.      Connect the circuit as per the circuit diagram.

2.      Keep each source independently and calculate current through the response.

3.      Verify the theoretical value with practical value.

RESULT:

         Thus the Superposition theorem is verified for the given circuit.

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