Thevenin's Theorem

In this lab, Thevenin's Theorem not only is investigated experimentally but it is determined analytically as well. A variable load resistor is connected between points a and b.

Figure 1: Thevenin's Theorem Circuit

All of resistors are measured by a digital Ohmmeter, and those are written by red color (Fig 1).

Figure 2: Calculation of Thevenin's Voltage

According to measured resistors in the above circuit, Thevenin's Voltage is calculated.

(2.17 + 4.58)*I1 = 2-5
(6.65 + 6.69)*I2 = -5         , I1 = - 0.444 A , I2 = - 0.375 A

 Vc - 4.58*I1 + 6.69*I2 = Vd , Vc - Vd =  Vth = 4.58*(-0.444) - 6.69*(-0.375) = 0.475 v

Theoretical Thevenin's voltage is 0.475 v , and experimental Thevenin's voltage is 0.47 v (Fig 1).

Percent Thevenin's Voltage = [(0.475-0.47)/0.475]*100 = 1.1%

Percent Thevenin's Resistor = [(7.4 - 7.31)/7.4]*100 = 1.22%  

Figure 3: Thevenin's Voltage is measured 0.47 volts

When the load resistor changes, its drop voltage will measured by a digital voltmeter, and it records in order to determine drop power of the load resistor.

 

Load Resistor (Ω)	Drop Load Voltage (v)	Drop Load Power (W)
2.17E+03	0.108	5.38E-06
3.53E+03	0.153	6.63E-06
4.62E+03	0.183	7.25E-06
5.61E+03	0.204	7.42E-06
6.80E+03	0.227	7.58E-06
7.40E+03	0.238	7.65E-06
8.02E+03	0.247	7.61E-06
9.80E+03	0.27	7.44E-06
1.78E+04	0.334	6.27E-06

When P(load) is maximum?

At now, circuit has a voltage source equal Thevenin's voltage, and a resistor equal Thevenin's resistor. In this situation, when R(load) is equal with Rth, P(load) will be maximum.

P(load) = [(Vload)^2] / RL , V(load) = [RL / (RL+Rth)]*Vth → P(load) = (RL)*[Vth / (RL+Rth)]^2

Derivative of P(load) relative to RL equal zero is [(RL+Rth)^2] - (RL)*[2*(RL+Rth)] = 0

(RL+Rth) - 2*RL = 0 , RL = Rth

According to the above table, P(load) is maximum when RL is equal 7.4 k.

This is the formula P(load) = (RL)*[0.47/(7400 + RL)]^2 that graph figure 4 follows.

Figure 4: Load Power vs Load Resistor

According to above table, RL is chosen exactly equal Rth, and under this situation load power is maximum.