A cell of emf \( E \) and internal resistance \( r \) is connected to an external variable resistance \( R \). Plot a graph showing the variation of terminal voltage \( V \) of the cell as a function of current \( I \), supplied by the cell. Explain how the emf of the cell and its internal resistance can be found from it.
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To determine the emf and internal resistance of a cell, measure the terminal voltage at different currents and plot \( V \) versus \( I \). The slope and the intercept of the graph give the internal resistance and emf, respectively.
The terminal voltage ($V$) of a cell is defined by the equation $V = E - Ir$, where $E$ is the electromotive force (emf), $r$ is the internal resistance, and $I$ is the current supplied.
When the external resistance ($R$) changes, both the current ($I$) and terminal voltage ($V$) vary. Consequently, the relationship between terminal voltage and current is linear. The slope of the $V$ vs. $I$ graph is $-r$, and the $y$-intercept is $E$.
Graph characteristics:
1. The slope of the $V$ vs. $I$ graph is equal to the negative of the internal resistance ($-r$).
2. The $y$-intercept of the graph represents the emf ($E$), as $V = E$ when $I = 0$.
Determining $E$ and $r$ from the graph:
1. Emf ($E$): Identify the $y$-intercept. This value is the emf, as $V = E$ when $I = 0$.
2. Internal Resistance ($r$): Calculate the magnitude of the slope of the graph. The slope is equal to $-r$, so its absolute value gives $r$.
For instance, in the provided graph, the slope is $-2$, indicating an internal resistance ($r$) of $2 \, \Omega$. The $y$-intercept is $6 \, \text{V}$, representing an emf ($E$) of $6 \, \text{V}$.
