[Circuits] Calculating the Thevenin Equivalent #1

[ainster31]

Homework Statement

Homework Equations

The Attempt at a Solution

I got ##R_{ th }=4\quad Ω## easily but I am having trouble finding ##V_{th}##. Assume the negative terminal of the 32V voltage source is ground. Here is the nodal analysis at node 1:

$$\frac { 32-V_{ 1 } }{ 4 } +2=\frac { V_{ 1 } }{ 12 } +V_{ 1 }-V_{ 2 }$$

But I only have one equation and there are two variables.

 

[gneill]

When you remove the load R_L, and after assigning a common reference node, there's only one essential node remaining. So you should have one equation in one unknown.

Note that with the load removed there will be no current flow through the 1 Ω resistor...

 

[ainster31]

When you remove the load R_L, and after assigning a common reference node, there's only one essential node remaining. So you should have one equation in one unknown.

Note that with the load removed there will be no current flow through the 1 Ω resistor...

Opps, I should've added that I'm trying to find the voltage between (a) and (b).

##V_1## is the voltage on the node in between the 4 ohm and 12 ohm resistor and ##V_2## is the voltage of (a). (b) is ground.

If there is no current flow through the 1 ohm resistor, does that mean that the voltage of ##V_1## and ##V_2## is the same?

 

[gneill]

Opps, I should've added that I'm trying to find the voltage between (a) and (b).

##V_1## is the voltage on the node in between the 4 ohm and 12 ohm resistor and ##V_2## is the voltage of (a). (b) is ground.

If there is no current flow through the 1 ohm resistor, does that mean that the voltage of ##V_1## and ##V_2## is the same?

Yup. No current means no potential drop.

 

[rezeew]

I would recommend using Kirchhoff's Voltage Law (KVL) to solve for the Thevenin voltage, Vth. This law states that the sum of all voltages around a closed loop in a circuit is equal to zero. In this case, the closed loop can be formed by starting at the negative terminal of the 32V voltage source, going through the 4Ω resistor, the 12Ω resistor, and back to the negative terminal. This should give you the following equation:

-32 + Vth + 12(Vth-V2) + 4V2 = 0

From here, you can solve for Vth and then use the Thevenin theorem to find the equivalent circuit. Remember that the Thevenin voltage is the open circuit voltage at the terminals, so you can remove any loads or resistors connected to the circuit before solving for Vth.

I would also recommend double checking your nodal analysis equation to make sure it is set up correctly. It's always a good idea to have multiple methods for solving a problem in case one doesn't work out.