A 50-Ωresistor is connected across a battery, and a 26-mA...

A $50-\Omega$ resistor is connected across a battery, and a $26-\mathrm{mA}$ current flows. When the resistor is replaced with a $22-\Omega$ resistor,
43 mA flows. Find the battery's voltage and internal resistance.

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Key Concepts

Battery Modeling

This involves representing a battery as an ideal voltage source (EMF) in series with an internal resistance. This model explains how the battery's output voltage decreases as current increases due to the voltage drop across the internal resistance, and it provides the foundation for setting up equations in circuit analysis.

Ohm’s Law

Ohm’s Law forms the basis of circuit analysis by relating voltage, current, and resistance through the formula V = IR. In problems involving battery internal resistance, it allows for the creation of equations based on the measured currents and external resistances to find unknown values like battery voltage and internal resistance.

Series Circuit Analysis

In a series circuit, current remains constant through all components, and the total voltage is the sum of voltage drops across each element. This concept is key when analyzing circuits with a battery, its internal resistance, and an external resistor, enabling the formulation of equations that reflect the voltage distribution in the circuit.

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