Thevenin equivalent circuit with a load

In summary, to show that the maximum power is delivered to the external resistor when R=R1 in a circuit with a battery of fixed emf E and internal resistance R1, we can calculate the current and voltage across the resistor and use Ohm's law to find the power equation. Differentiating with respect to R and setting it to 0 shows that R=R1 is the optimal resistance for maximum power delivery.
  • #1
curiousmuch
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Homework Statement


Show that if a battery of fixed emf E and internal resistance R1 is connected to a variable external resistance R, the maximum power is delivered to the external resistor when R=R1


Homework Equations


Power = R * I^2


The Attempt at a Solution


We can think of problem as divide-by-two voltage divider and the power transferred to load is maximized when the load resistance is equal to the Thevenin resistance, but I don't know how to proceed.
 
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  • #2
The power delivered to the external resistor is given by P = I^2*R where I is the current flow. We can calculate the current by applying Ohm's law; I = V/R where V is the voltage across the resistor. The voltage across the resistor is given by V = E - Ir1, where r1 is the internal resistance of the battery. Therefore, P = (E-Ir1)^2/R. Differentiating with respect to R gives us: dP/dR = -2(E-Ir1)*r1/R^2. Setting this to 0 and solving for R gives us R=R1. Hence, the maximum power is delivered when R=R1.
 

1. What is a Thevenin equivalent circuit with a load?

A Thevenin equivalent circuit with a load is a simplified representation of a complex circuit that contains a single voltage source and a single resistor, known as the Thevenin voltage and Thevenin resistance, respectively. This equivalent circuit is used to analyze and predict the behavior of a more complicated circuit, and is especially useful for calculating the voltage and current at a specific point in the circuit.

2. How do you calculate the Thevenin voltage and resistance?

The Thevenin voltage (Vth) is calculated by removing the load from the original circuit and measuring the voltage across the load terminals. The Thevenin resistance (Rth) is calculated by shorting all voltage sources in the original circuit and finding the total resistance between the load terminals.

3. What is the purpose of a load in a Thevenin equivalent circuit?

The load in a Thevenin equivalent circuit represents the part of the original circuit that we are interested in analyzing. It can be any combination of components, such as resistors or capacitors, and is used to determine the voltage and current at a specific point in the circuit.

4. How can Thevenin equivalent circuits be applied in real-world situations?

Thevenin equivalent circuits are commonly used in circuit analysis and design, as well as in troubleshooting and testing electronic systems. They allow engineers to simplify complex circuits and make calculations more manageable, saving time and resources.

5. What are the limitations of Thevenin equivalent circuits?

Thevenin equivalent circuits assume linear behavior of components and do not take into account non-linear effects such as saturation or temperature dependence. They also do not account for changes in the circuit due to external influences or varying conditions. Additionally, they may not accurately represent circuits with multiple sources or non-linear components.

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