A cell supplies a current I, through a resistance R1 and a current I2 through a resistance R2 th

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A cell supplies a current I, through a resistance R1 and a...

A cell supplies a current $\mathrm{I}$, through a resistance $\mathrm{R}_{1}$ and a current $\mathrm{I}_{2}$ through a resistance $\mathrm{R}_{2}$ the internal resistance of a cell is... (A) $\mathrm{R}_{2}-\mathrm{R}_{1}$ (B) $\left\{\left(\mathrm{I}_{1}+\mathrm{I}_{2}\right) /\left(\mathrm{I}_{1}-\mathrm{I}_{2}\right)\right\} \mathrm{R}_{1} \mathrm{R}_{2}$ (C) $\left\{\left(\mathrm{I}_{1} \mathrm{R}_{2}-\mathrm{I}_{2} \mathrm{R}_{1}\right) /\left(\mathrm{I}_{1}-\mathrm{I}_{2}\right)\right\}$ (D) $\left\{\left(\mathrm{I}_{2} \mathrm{R}_{2}-\mathrm{I}_{1} \mathrm{R}_{1}\right) /\left(\mathrm{I}_{1}-\mathrm{I}_{2}\right)\right\}$

A cell supplies a current $\mathrm{I}$, through a resistance $\mathrm{R}_{1}$ and a current $\mathrm{I}_{2}$ through a resistance $\mathrm{R}_{2}$ the internal resistance of a cell is...
(A) $\mathrm{R}_{2}-\mathrm{R}_{1}$
(B) $\left\{\left(\mathrm{I}_{1}+\mathrm{I}_{2}\right) /\left(\mathrm{I}_{1}-\mathrm{I}_{2}\right)\right\} \mathrm{R}_{1} \mathrm{R}_{2}$
(C) $\left\{\left(\mathrm{I}_{1} \mathrm{R}_{2}-\mathrm{I}_{2} \mathrm{R}_{1}\right) /\left(\mathrm{I}_{1}-\mathrm{I}_{2}\right)\right\}$
(D) $\left\{\left(\mathrm{I}_{2} \mathrm{R}_{2}-\mathrm{I}_{1} \mathrm{R}_{1}\right) /\left(\mathrm{I}_{1}-\mathrm{I}_{2}\right)\right\}$

Key Concepts

Electromotive Force (emf) and Internal Resistance

A real cell is modeled as an ideal voltage source (emf) in series with an internal resistance. The emf is the maximum voltage the cell can provide when no current flows, while the internal resistance represents the inherent opposition to current flow inside the cell, causing a voltage drop under load conditions.

Terminal Voltage

Terminal voltage is the voltage that is available across the cell's terminals when a current is drawn. It is determined by subtracting the voltage drop across the internal resistance (which is the product of the current and the internal resistance) from the emf, thereby reflecting the cell’s performance under load.

Ohm’s Law

Ohm’s law states that the voltage across a resistor is equal to the product of the current flowing through it and its resistance (V = IR). This fundamental principle is used to relate the voltage drops across various resistive elements in a circuit, including the external load and the internal resistance of a cell.

Load Variation Method

By connecting different load resistances to a cell and measuring the corresponding currents and terminal voltages, one can derive the internal resistance. This method involves setting up equations using Ohm’s law and the concept of terminal voltage, and then eliminating the emf by comparing different load conditions to solve for the internal resistance.

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