- Introduction
The dc circuit theories of Norton and Thevenin are investigated in this practical. The Thevenin theorem states that any network of resistors and sources (voltage and current) when viewed from any two points in a network can be replaced by an equivalent circuit of a single resistance (Thevenin Resistance) in series with a voltage source (Thevenin voltage). Similarly, Norton’s theorem is aimed at replacing the network of resistors and sources with an equivalent circuit of a constant current source in parallel with a resistance.
- Results
Experimental data
The Thevenin resistance of the circuit is calculated by replacing the voltage source with a short circuit. The resistance as seen from the terminals AB is a parallel combination of 1.5k Ω and 3k Ω in series with 500 Ω. The result of this in series with a parallel combination of 300 Ω and 750 Ω gives the total resistance Rth or RAB of the circuit.
R1 = (1500//3000) Ω + 500 Ω = 1500
R2 = (R1 //300) Ω + 750 Ω = 1000 Ω = Rth
Calculating the Thevenin Voltage
The Thevenin voltage is calculated by replacing the voltage source in the circuit and opening the terminals AB of the circuit. The Thevenin voltage is the voltage seen from the terminal AB of the circuit. This voltage is obtained by calculating the voltage drop across the 300Ω resistor. Since the circuit is open at AB, no current flows through the 750Ω resistor. Using mesh current analysis, the current flowing through the 500Ω resistor is also the same current flowing through the 300Ω resistor and is 3.7mA. Thus the voltage drop across the 300Ω resistor is (300Ω X 3.7mA) which gives 1.11V.
The equivalent Thevenin circuit is drawn below.
Figure 1 showing the Thevenin equivalent of the circuit
Calculating the Norton Current
Since the terminals have been shorted, current flows through the 750Ω resistor. Making reference to the 3.7mA current that was calculated flowing through the 500Ω resistor when the Thevenin voltage was calculated above, the short circuit current is calculated using current divider principle.
IR = I1R1
I1 = IR / R1
R is the total resistance of the circuit with value 214.28Ω, I is the current flowing through the 500Ω resistor and R1 is the 750Ω resistor.
This results in a value of 1.05mA for the Norton current.
Percentage Difference
The percentage difference between the calculated values were calculated using the formula
Percentage difference= calculated value-measured valuecalculated vaue X 100
Graph of PL on the y-axis against RL on the x-axis.
Figure 2 showing Graph of PL(W) against RL (Ω)
According to the maximum power transfer theorem, a resistive load will absorb maximum power from a network when the load resistance is equal to the resistance of the network seen from the output terminals when all the energy sources are removed. This simply means that the resistive load will absorb maximum power when its value equals the Thevenin resistance.
- Maximum Power Transfer
Maximum power is absorbed by RL when RL = RAB
PLmax = Vab2
PLmax= Vab24RL
Plugging the calculated values of Vab = 1.11V and RL = 1000 Ω,
PLmax = 3.01 X 10-4 W
The maximum power drawn is the peak of the graph of power against the resistance. The peak of the graph corresponds to the point (1000Ω, 3.04 X 10-4 W) i.e. the power is 3.04 X 10-4 W when the load resistance RL is 1000 Ω.
The calculated value of the maximum power is slightly different from the measured value. It is noticeable that the difference is such that the measured value is higher that the calculated value. This increase in the measured value can be attributed to the internal resistance of the measuring device.
The shape of the graph obtained is very similar to what is expected. The expectation is that as the value of the load resistance increases, the absorbed power should also increase. However at the point where the load resistance equals the Thevenin resistance is expected to be a turning point since the maximum value of the power is obtained here.
Note
Kuphaldt, Tony R. Lessons In Electric Circuits, Volume I - DC . Open Book Project, 2005.
