Which of the following truly represents the Thevenin’s equivalent circuit when a voltage source of 24 V undergoes a voltage drop of 0.6 V due to a load current of 1A?
V th = 24V R th = 0.6 Ω
Understanding Thevenin's theorem is crucial for simplifying complex electrical circuits into a simpler equivalent form. This equivalent circuit consists of a single voltage source, known as the Thevenin voltage (\(V_{th}\)), in series with a single resistor, called the Thevenin resistance (\(R_{th}\)). This problem requires us to determine these two parameters based on the given information about a voltage source and its behavior under load.
Thevenin Voltage (\(V_{th}\)) Determination
The Thevenin voltage, \(V_{th}\), represents the open-circuit voltage across the terminals of the circuit where the load would be connected. In this problem, we are given that the voltage source itself is 24 V. This value represents the ideal or open-circuit voltage of the source before any load is connected or any internal resistance causes a drop.
- The problem states: "a voltage source of 24 V".
- This 24 V is the inherent voltage of the source when no current is drawn, or effectively, the open-circuit voltage.
- Therefore, the Thevenin voltage \(V_{th}\) is equal to the original source voltage.
So, \(V_{th} = 24\, \text{V}\).
Thevenin Resistance (\(R_{th}\)) Calculation
The Thevenin resistance, \(R_{th}\), represents the equivalent resistance looking back into the circuit from the load terminals, with all independent voltage sources short-circuited and all independent current sources open-circuited. We can determine \(R_{th}\) by observing how the source voltage changes when a current is drawn, which indicates an internal resistance causing a voltage drop.
We are given the following information:
- Original voltage source = 24 V
- Voltage drop due to a load current = 0.6 V
- Load current = 1 A
The voltage drop of 0.6 V occurs across the internal resistance of the source (which is \(R_{th}\)) when a load current of 1 A flows through it. According to Ohm's Law, the voltage drop across a resistor is the product of the current flowing through it and its resistance.
The formula for Ohm's Law is: \(V = I \times R\).
In our case, the voltage drop (\(V_{drop}\)) is 0.6 V, and the current (\(I_{load}\)) causing this drop is 1 A. The resistance causing this drop is the Thevenin resistance (\(R_{th}\)).
We can write the equation as:
\(V_{drop} = I_{load} \times R_{th}\)
Now, let's substitute the given values into the equation:
\(0.6\, \text{V} = 1\, \text{A} \times R_{th}\)
To find \(R_{th}\), we rearrange the equation:
\(R_{th} = \frac{0.6\, \text{V}}{1\, \text{A}}\)
Performing the division:
\(R_{th} = 0.6\, \Omega\)
Summary of Thevenin's Equivalent Circuit Parameters
Based on our calculations, the Thevenin equivalent circuit parameters are:
- Thevenin Voltage (\(V_{th}\)): This is the open-circuit voltage of the source, which is given as 24 V.
- Thevenin Resistance (\(R_{th}\)): This is calculated from the voltage drop across the internal resistance due to the load current, resulting in 0.6 Ω.
Therefore, the Thevenin's equivalent circuit truly represents:
| Parameter | Value |
|---|---|
| \(V_{th}\) | 24 V |
| \(R_{th}\) | 0.6 Ω |
This means the correct representation of the Thevenin's equivalent circuit is \(V_{th} = 24\, \text{V}\) and \(R_{th} = 0.6\, \Omega\).
Important Questions from Thevenin's Theorem
- Which linear circuit can be used as an equivalent circuit for a single voltage source and a series resistance ?
Which theorem is advantageous, when we have to determine the current in a particular element of a linear bilateral network particularly when it is desired to find the current which flows through a resistor for its different values?
Which of the following theorem states that "a linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source VTH in series with a resistor RTH", where VTH is the open circuit voltage at the terminals and RTH is the input or equivalent resistance at the terminals, when the independent sources are turned off
Which of the theorem does provide a mathematical technique for replacing a given network, as viewed from two output terminals, by a single voltage source with a series resistance?
Thevenin's Theorem states that, any linear active Double terminal network containing voltage and resistance sources can be replaced by a ________ Voltage source in _______ with ________ resistance.
