We are able to use Thevenin's Theorem to reduce a complicated into a simple circuit such as below with a Voltage and a resistor that represent the complicated circuit.
We are given a circuit and we need to measure the Thevenin equivalent voltage and resistance as shown below
The Thevenin Resistance can be detremined from R_TH=V_oc/I_sc where I is the current measured as short circuit at the two points
The given element has the theoratical value of
R_c1 | R_c2 | R_c3 | R_L1 | Vs1 | Vs2 |
100Ohm | 39Ohm | 39Ohm | 680Ohm | 9V | 9V |
First we used nodal analysis to find the open-circuit voltage
we got a equation:
(Vx-Vs2)/Rc2 + (Vx-Vs1)/Rc1+Vx/Rcl=0
Vx has the value of 8.64V, which is the Thevenin Voltage
Next, we calculate the voltage V_y in the fugure. Then find the short-circuit current use it to compute the Thevenin resistance
(Vx-Vs2)/Rc2 +(Vx-Vs1)/Rc1+Vx/Rc1+Vy/Rc3=0
Vy=5.11V
Isc=5.11/39=0.131A
Rth=66Ohm
After knowing the R_th and V_th. We can know draw another circuit that contains two resistors in series, which are R_th and R_load. We can use a voltage divider since we know the voltage drop across the R_load is 8V to find the theoretical value of R_load
R_L2=825Ohm
After that we just device the experiment and measure all the components and the value of voltage across different components
Component | Nominal Value | Measured Value | Power Rating |
R_th(Ohm) | 66 | 66.6 | 0.3W |
R_L2,min(Ohm) | 825 | 822 | 0.3W |
V_TH | 8.64 | 8.64 | x |
Now, we can build the THevenin Equivalent Circuit on the Breadboard and record data
Configuration | Theoretical Value | Measured Value | Percent Error |
RL2=RL2,min | VLoad2=8V | 7.99 | 0.12% |
R=L2=infinite | VLoad2=8.64 | 8.64 | 0% |
Measured Value
Component | Nominal Value | Measured Value | Power Rating |
R_c1 | 100Ohm | 99.6Ohm | 0.25W |
R_c2 | 39Ohm | 39.0Ohm | 0.25W |
R_c3 | 339Ohm | 4.02Ohm | 0.25W |
R_L1 | 680Ohm | 679 Ohm | 0.5W |
V_s1 | 9V | 9.07V | 18W |
V_s2 | 9V | 8.97V | 18W |
Building the Original Circuit
We obtained the following data
Configuration | Theoretical Value | Measured Value | Percent Error |
R_L2=R_L2min | Vload2=8.64 | 8.31V | 3.90% |
R_L2=infinite | Vload2=8.64 | 8.62V | 0.23% |
Configuration | V_load2 (V) | P_load2 (W) |
0.5R_th | 2.87 | 0.2496 |
R_th | 8.31 | 1.0463 |
2R_th | 5.74 | 0.2496 |