Question

A condenser of $2 \,\mu F$ capacitance is charged steadily from $0$ to $5 C$ Which of the following graph represents correctly the variation of potential difference $(V)$ across it's plates with respect to the charge $( Q )$ on the condenser?

• A.
• B.
• C.
• D.

Answer 1

The Correct Option is A

To solve this problem, we need to understand the relationship between the charge (Q) on a capacitor and the potential difference (V) across its plates. The fundamental formula governing this relationship is given by:

\(V = \frac{Q}{C}\)

Where:

• \(V\) is the potential difference across the capacitor.
• \(Q\) is the charge on the capacitor.
• \(C\) is the capacitance of the capacitor.

 

Given in this problem, the capacitance \(C = 2 \,\mu F = 2 \times 10^{-6} \,F\). The charge \(Q\) ranges from 0 to 5 C.

Substituting \(Q\) and \(C\) in our formula:

\(V = \frac{Q}{2 \times 10^{-6}}\)

This implies that \(V\) is directly proportional to \(Q\). Therefore, the graph of \(V\) vs. \(Q\) will be a straight line passing through the origin, indicating a linear relationship with a constant slope.

Now let's analyze the provided options to identify the correct graph:

Among the given options, only the graph which shows a straight line beginning at the origin represents the direct proportionality of \(V\) to \(Q\).

Conclusion: The correct graph is a line that passes through the origin with a positive slope, matching the image labeled as the correct answer: