Thevenin Problem Homework: Find Current When RL is Short

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In summary, the conversation discussed how to find the current when the load resistance (RL) is set to open and when it is set to a short circuit. The first step is to use the voltage divider equation to find the voltage when RL is open. Then, to find the current when RL is a short circuit, the total current (ITOT) is found using the formula I=V/R, and the current divider formula is used to determine the current through the specific resistor. The conversation also clarified the labeling of the parallel resistors in Diagram B and explained how to use the current divider formula.
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erok81
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Homework Statement



This one has a few parts, so let's start with part a. See attachment for circuit. I've got two drawings in the attachment. I'll label them A and B. Image A is the original circuit.

Homework Equations



None.

The Attempt at a Solution



My first step is to find set RL to open. I can use a voltage divider equation and find the voltage to be 16V.

The next (which is where I am stuck) is to find RL as a short. Shown by image B. My professor wasn't the best in showing this as he used some trick I have no clue how solved this way.

I can find ITOT using...

[itex]I=\frac{V}{R} \Rightarrow \frac{24}{3+6//4}[/itex]

Solving for ITOT gives me 4.4A. My professor used this value and somehow came up with the current over the 4Ω resistor.

Then plugged it into..

[itex]R_{th} = \frac{V_th}{I_{short}}[/itex]

To find the Thevenin equivalent.

How does one find the current when RL is a short?
 

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  • #2
Did you mean for the parallel resistors in Diagram B to be 6R and 4R? They are labeled 6R and 3R currently.

Knowing the circuit series current allows you to determine how the current will split when it enters a parallel connection. The general way to do this is using the current divider formula:

[itex]I_{n}[/itex] = [itex]I_{s}[/itex] * [itex]\frac{R_{other}}{(R_{other} + R_{n})}[/itex]

Where:

[itex]R_{other}[/itex] is the total resistance of the other resistors, [itex]R_{n}[/itex] is the resistance which you wish to find the current through, [itex]I_{s}[/itex] is the current being divided and [itex]I_{n}[/itex] is the current you want to find.
 

1. What is the Thevenin theorem?

The Thevenin theorem is a fundamental principle in electrical engineering that states that any linear circuit with voltage and current sources can be replaced by an equivalent circuit consisting of a single voltage source and a single resistor connected in series.

2. How do I find the Thevenin equivalent circuit for a given circuit?

To find the Thevenin equivalent circuit, you need to follow these steps:

  1. Remove the load resistor (RL) from the original circuit.
  2. Calculate the open-circuit voltage (Voc) across the load resistor terminals.
  3. Calculate the equivalent resistance (Req) between the load resistor terminals.
  4. Draw the Thevenin equivalent circuit with the calculated Voc and Req values.

3. What is the purpose of finding the Thevenin equivalent circuit?

The Thevenin equivalent circuit allows for simplification of a complex circuit into a single voltage source and resistor, making it easier to analyze and calculate the behavior of the circuit. It also allows for easier circuit design and troubleshooting.

4. How do I find the current when RL is short in the Thevenin equivalent circuit?

To find the current when RL is short, you can use the Thevenin theorem formula: I = Voc/Req, where Voc is the open-circuit voltage and Req is the equivalent resistance. Simply plug in the values for Voc and Req and solve for I. In some cases, you may need to use the current divider rule to calculate the current.

5. What is the significance of finding the current when RL is short?

Finding the current when RL is short allows you to determine the maximum current that can flow through the load resistor in the Thevenin equivalent circuit. This is important for determining the power dissipation and potential damage to the circuit components. It also helps in selecting the appropriate load resistor for the circuit.

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