EE2721 Electric Circuit Analysis

Group 5

Introduction:

The objectives of this experiment are to

Verify Kirchhoff’s laws

Determine the equivalent resistance of a network

Study the maximum power transfer theorem

Apparatus:

DC power supply

Multi-meter (DMM)

Experimental board

Experiment 1:(Kirchhoff’s laws)

Theory:

According to the Principle of conservation of Charges, since charges do not accumulate at any point in a network, the charges cannot be created or destroyed.

This bring the Kirchhoff’s First Law, the algebraic sum of the current at a junction of a circuit is zero. Therefore, the current arriving a junction equals the current leaving the junction.

This law also assumed to be positive if it flows into a point and negative if it flows out from the point.

There is also a Kirchhoff’s second law relates the total e.m.f in a closed loop.

Round a closed loop, the algebraic sum of the e.m.f is equal to the algebraic sum of the products of the current and resistance.

Procedure:

The experimental board was connected to the DC power supply as follow

2. The DC supply was adjusted to keep the voltage across Nodes A and C to 5V

3. The voltage across the branched that connect to Node B were measured, the data

we took

+

+

=0.1330+(-0.0398)+(-0.0936)=-4x

A

4. Step 3 was repeated for Node M, the data we took

+

+

=0.06643+(-0.1078)=0.03995=-1.42x

A

The results we took both are very close to zero. The above result show that it obey the Kirchhoff’s first law(current law).

5. The voltage across AC was adjusted to 5V, then the voltage around loop AMBCA was measured, the data we took

6. The voltage around loop ABMCA was measured, the data we took

The results we took both are very close to zero. The above result show that it obey the Kirchhoff’s second law(voltage law).

Experiment 2:(Equivalent resistance)

Theory:

The transformation is used to establish equivalence for networks with three terminals. Where three elements terminate at a common node and none are sources, the node is eliminated by transforming the impedances. For equivalence, the impedance between any pair of terminals must be the same for both networks. The equations given here are valid for complex as well as real impedances

Procedures:

The power supply was turned off. And the multimeter was used to measured the equivalent resistance

of the network in the previous circuit we used

=21.5Ω

The power supply was removed, we measured again the equivalent resistance

=28.4Ω

The result in step 1 is smaller than in step 2.In step 1 , the power supply has not been removed, and it consists internal resistance. As it connects parallel to

the circuit, the equivalent resistance will be smaller than without parallel internal resistance.

The star-to delta or the delta –to –star transformation was used to calculate the equivalent resistance of network shown in figure 3.

equivalent resistance of

:

The

we calculate is close to step 1 but smaller than step 2. When we calculate the equivalent resistance of

,we don’t know the internal resistance of power supply and we assumed the internal resistance is zero and ignore it in calculation, so the result we calculate is similar to data with removal of power supply.

Experiment 3(Maximum power transfer theorem)

Procedures:

The circuit as shown in figure 7 with

was connected and the power supply was adjusted to 5V.

The load

from 1KΩ to 25KΩ resistances were varied in small but suitable step. The corresponding values of

and

in each step were recorded.

=5KΩ

The power delivered to the load against

was plotted

Maximum power: 1.275 mW

4.88

Total resistance:4.88+5=9.88

=10KΩ(with

varying from 5KΩ to 15KΩ)

Maximum power: 0.6127mW

9.2

Total resistance:9.2+10=19.2

=20KΩ(with

varying from 15KΩ to 25KΩ)

Maximum power: 0.0215mW

20.05

Total resistance:20.05+20=40.05

Discussion:

aI) minimum sources voltage:

V=400x2x

=40v

aII) there is not significant risk of this type of accident to occur, as the voltage of personal computer is 17v, it is smaller than the minimum source voltage that can produce electrical shock.

b) The criterion for maximum power transfer from a source to a load is the load resistance equals to the internal resistance of the source. If we are free to select

without changing the source voltage, we can decrease the

in order to maximize the power delivered to the load.

E=i(R+

iE=

=

=

The smaller the

, the higher the power supply

C)

=

=

=

The maximum power output occurs when

=

=0

=0

=2R

=

The maximum power output

=

=