Question

A student measures the terminal potential difference (V) of a cell (of emf $\varepsilon $ and internal resistance r) as a function of the current $(I)$ flowing through it. The slope, and intercept, of the graph between V and I, then, respectively, equal

• A. $-r$ and $\varepsilon $
• B. $r$ and $-\varepsilon $
• C. $-\varepsilon$ and $r$
• D. $\varepsilon $ and $-r$

Answer 1

The Correct Option is A

 To solve the problem of determining the slope and intercept of the graph between the terminal potential difference (V) and current (I) for a cell with electromotive force (emf) \(\varepsilon\) and internal resistance \(r\), we can start with the equation for terminal voltage:

The terminal potential difference \((V)\) is given by:

\[V = \varepsilon - Ir\]

This equation is in a linear form similar to \(y = mx + c\), where:

• \(y\) is the dependent variable which, in this case, is \(V\).
• \(x\) is the independent variable, which in this case is \(I\) (current).
• The slope \((m)\) is represented by \(-r\) (negative internal resistance).
• The y-intercept \((c)\) is represented by \(\varepsilon\) (emf of the cell).

Therefore, analyzing the equation, we find that:

• Slope: The slope of the graph of V versus I is \(-r\).
• Intercept: The y-intercept of the graph is the emf, \(\varepsilon\).

Thus, the correct answer is that the slope is \(-r\) and the intercept is \(\varepsilon\). Option:

\(-r\) and \(\varepsilon\)

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