A resistor with resistance R is connected to a battery that...

A resistor with resistance $R$ is connected to a battery that has emf $12.0 \mathrm{~V}$ and internal resistance $r=0.40 \Omega .$ For what two values of $R$ will the power dissipated in the resistor be $80.0 \mathrm{~W} ?$

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Key Concepts

Power Dissipation in Resistive Circuits

Power dissipation in a resistor is the process of converting electrical energy into heat, and it is quantified by the formula P = I^2R or P = V^2/R. Understanding this concept is essential for determining how much energy is converted into heat and ensuring that components can handle the thermal load.

Equivalent Circuit Analysis

Equivalent circuit analysis involves representing a complex circuit with simpler components to make calculations more manageable. In the context of power sources with internal resistance, it is important to consider both the external resistance and the internal resistance to accurately determine the overall behavior and power distribution of the circuit.

Ohm's Law

Ohm's Law describes the linear relationship between voltage, current, and resistance in an electrical circuit. It states that the voltage across a resistor is equal to the product of the current flowing through it and its resistance (V = IR), serving as a fundamental principle for analyzing electric circuits.

Internal Resistance

Internal resistance refers to the resistance within a battery or any power source that impedes the flow of current. This concept is crucial because it affects the terminal voltage of the battery under load and influences the efficiency of power delivery in a circuit.

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