thevenin's theorem explanation | Thevenin's Theorem Solved Example Problem

Summary

This video explains how to calculate the current through an 8-ohm resistor using Thevenin's Theorem. The process involves finding the Thevenin equivalent resistance (Rth) and Thevenin equivalent voltage (Vth) by first turning off independent sources and applying Kirchhoff's Voltage Law (KVL). After calculating Rth and Vth, these values are substituted into Thevenin's equivalent circuit to find the load current through the 8-ohm resistor, which is 1.446 amps. For more details, viewers are directed to install the app and access free electrical circuit notes.

Takeaways

• 📘 The video explains how to find the current through an 8-ohm resistor using Thevenin's theorem.
• 🔌 Thevenin's theorem states that a linear two-terminal circuit can be replaced by a voltage source (Vth) in series with a resistor (Rth).
• 🛠️ Vth is the open circuit voltage at the terminals, and Rth is the equivalent resistance when independent sources are turned off.
• 📊 The current through the load resistor RL can be calculated using I = Vth / (Rth + RL).
• 🔄 To find Rth, turn off all independent sources and calculate the equivalent resistance of the remaining circuit.
• 🔍 The calculation involves finding the parallel resistance of 6 ohms and 10 ohms, which gives an Rth of 3.75 ohms.
• 📏 To find Vth, apply Kirchhoff’s Voltage Law (KVL) to the outer loop of the circuit.
• ⚡ The current in the circuit is found to be 0.5 amperes using KVL.
• 🖋️ The value of Vth is calculated as 17 volts using KVL in the inner loop.
• 📐 After finding both Vth and Rth, the current through the 8-ohm load resistor is calculated as 1.446 amperes.

Q & A

What is Thevenin's theorem?

Thevenin's 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). Vth is the open circuit voltage at the terminals, and Rth is the equivalent resistance at the terminals when all independent sources are turned off.

What is the purpose of using Thevenin's theorem in the circuit?

Thevenin's theorem simplifies complex circuits by allowing the calculation of the current through a specific resistor (load resistor) by reducing the circuit to a simple equivalent circuit with a voltage source and a series resistor.

How do you find the Thevenin resistance (Rth)?

To find Rth, you turn off all independent sources in the circuit, which means short-circuiting voltage sources and removing the load resistor (RL). Then, calculate the equivalent resistance of the circuit seen from the open terminals where RL was connected.

How is the equivalent resistance Rth calculated in this particular circuit?

In the circuit provided, the 6-ohm and 10-ohm resistors are in parallel. The equivalent resistance is calculated as 6 * 10 / (6 + 10), which gives 3.75 ohms.

How do you find the Thevenin voltage (Vth)?

To find Vth, remove the load resistor (RL), and calculate the open circuit voltage across the terminals where RL was connected. This is done using Kirchhoff's Voltage Law (KVL) to calculate the current and voltage in the circuit.

What is the formula for calculating the current through the load resistor using Thevenin’s theorem?

The current through the load resistor (I) is given by the formula: I = Vth / (Rth + RL), where Vth is the Thevenin voltage, Rth is the Thevenin resistance, and RL is the load resistor.

What value is calculated for the current through the 8-ohm resistor in this circuit?

The current through the 8-ohm resistor is calculated to be approximately 1.446 A using the formula I = Vth / (Rth + RL).

How is Kirchhoff’s Voltage Law (KVL) used in this circuit analysis?

KVL is applied to the outer loop to calculate the total voltage and current in the circuit. It states that the algebraic sum of all voltages around a closed loop is zero. This principle is used to find the current and voltage across components.

What values are substituted in the formula to calculate the current through the load resistor?

In the formula I = Vth / (Rth + RL), the values substituted are: Vth = 17 V, Rth = 3.75 ohms, and RL = 8 ohms, which gives the current I = 1.446 A.

What steps are involved in finding the Thevenin equivalent circuit?

The steps are: 1) Find the Thevenin resistance (Rth) by turning off all independent sources and calculating the equivalent resistance. 2) Find the Thevenin voltage (Vth) by removing the load resistor and calculating the open circuit voltage. 3) Replace the original circuit with the Thevenin equivalent circuit, consisting of Vth in series with Rth, and the load resistor RL. 4) Calculate the current through the load resistor.