A battery has an emf of 15.0 V. The terminal voltage of the...

A battery has an emf of $15.0 \mathrm{~V}$. The terminal voltage of the battery is $11.6 \mathrm{~V}$ when it is delivering $20.0 \mathrm{~W}$ of power to an external load resistor $R$. (a) What is the value of $R$ ?
(b) What is the internal resistance of the battery?

Key Concepts

Electrical Power in Resistive Circuits

Electrical power in resistive circuits is the rate at which electrical energy is converted to heat or work in a resistor. It is calculated using formulas that relate power to voltage and resistance, such as P = V²/R, and is essential for analyzing energy consumption and conversion in circuits.

Ohm's Law

Ohm's Law is a fundamental principle in electronics which states that the voltage across a resistor is directly proportional to the current flowing through it, with the constant of proportionality being the resistance. It is used to determine unknown quantities like current or resistance in a circuit.

Internal Resistance

Internal resistance is the inherent resistance within a power source that causes a voltage drop as current flows. It represents energy losses inside the source and results in the terminal voltage being lower than the electromotive force when a load is connected.

Terminal Voltage

Terminal voltage is the voltage output of a battery measured across its terminals when it is delivering current to a load. It is affected by the internal resistance of the battery and is generally lower than the electromotive force under load conditions.

Electromotive Force (EMF)

EMF is the energy provided per unit charge by a power source in an electrical circuit, typically represented by a battery. It is the open-circuit voltage of the device and reflects the maximum potential difference available before any internal losses occur.

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