TA: Your TA's name
Partner: Your partner's name
Thevenin and Norton Circuit Theory
Introduction
This experiment is aimed at putting to practice the Thevenin and Norton theories of dc resistor networks. These theories provide for techniques that make circuit analysis easier. In order to achieve this, a network of resistors connected to active sources is reduced to a single resistance which is connected in series with the voltage source. The single resistance is the Thevenin resistance of the network while the voltage source is the Thevenin voltage of the network. Norton’s Theorem also helps us simplify circuit analysis by replacing the network with a constant source of current connected in parallel with a resistor.
We achieved this by building the circuit with components of known value and taking readings of the voltage and power for varying values of load resistance using a multimeter. These measured values were then compared with calculated values and a percentage difference between the two sets of data was calculated. The almost negligible values of the percentage differences showed agreement between the measured values and the calculated values of the voltages, currents and resistance.
Data Table
Calculations
Thevenin Resistance
After removing the voltage source and replacing it with a jumper and opening the terminals AB, the resistance of the network as seen from the terminals is the Thevenin resistance.
RA // RB = RA X RBRA+ RB
Rth = (((1500Ω // 3000Ω) + 500Ω) // 300Ω) + 750Ω
Rth = 1000Ω
Thevenin Voltage
The voltage measured across the terminals AB when it is open circuited and the voltage source is present is the Thevenin voltage.
Using mesh analysis on the circuit, assuming a current I1 flows in the first mesh and current I2 flows in the second mesh, both in the clockwise direction, we write equations based on Kirchoff’s voltage law.
The algebraic sum of the voltage drops around a loop is zero.
10 – 1500I1 – 3000(I1 – I2) = 0 - - - 1
-500 I2 - 300 I2 – 3000(I2 – I) = 0 - - - 2
Solving equations 1 and 2 for I1 and I2,
I1 = 4.68mA
I2 = 3.70mA
I2 is the current flowing through the 300Ω resistor and the voltage drop across the resistor is
V = 300Ω X 3.70mA = 1.11 V
Vth = V = 1.11V
Norton Current
The Norton current is the short-circuit current flowing through a jumper connecting the two terminals A and B.
Making reference to I2 = 3.70mA as calculated above, the current splits at the junction according to the current division rule
IR = I1R1 = I2R2
R = 750Ω // 300Ω = 214.28Ω
The current flowing through the 750Ω resistor is
I1 = 3.70mA X 214.28Ω750Ω
Norton current I1 = 1.06mA
Percentage Difference
% DIFFERENCE= CALCULATED VALUE-MEASURED VALUECALCULATED VALUE X 100
% DIFFERENCE= (1.00k – 0.99k)Ω1.00kΩ X 100
= 1%
Maximum Power Absorbed
The maximum power absorbed by a load resistor in a dc circuit occurs when the value of the load resistor equals the Thevenin resistance of the resistor network. This value is calculated using the equation shown below
PLmax= Vth24 X RL
PLmax= 1.1124 X 1000
= 3.08 X 10-4W
Questions
The value of RL for the maximum power transfer is the value of R that corresponds to the peak of the graph. At the peak of the graph where PL = 4.12 X 10-4, RL = 1000. Therefore the value of RL for the maximum power transfer is 1000Ω.
The shape of the graph is as expected. In circuit, there is always a trade-off between efficiency and power. When a high efficiency is needed, the power of the circuit is reduced and vice versa. The power of the circuit in this case continued to increase until it peaked where RL = Rth. This point was the 50% efficiency level of the circuit. Further increase of power was no longer possible from this point onwards, only a drop. This is very similar to what is obtained here.
Sources of Error
The sources of error in this experiment are found in the resistances of the connecting wires. The resistance is directly proportional to the resistivity of the material and the length of the wire, and inversely proportional to the cross-sectional area of the wire. This means that the longer the wires used, the larger the resistance presented by the wires to the flow of current consequently, the greater the difference between the calculated and measured values.
Another source of error is introduced by the internal resistance of the voltage source. This also adds to the overall resistance of the circuit that is unaccounted for.
Conclusion
Despite the errors encountered in the course of the experiment, the whole aim of the experiment to practice the Norton and Thevenin circuit theory was achieved. I was able to relate the measured values of the Thevenin resistance, Thevenin voltage and Norton current to the calculated values in similarity. This is evidenced in the very small values of the percentage differences recorded for the values.
