Question

During the charging of a capacitor C in a series RC circuit, the typical variations in the magnitude of the charge \(q(t)\) deposited on one of the capacitor plates, and the current \(i(t)\) in the circuit, respectively are best represented by 

• A. Fig. I and Fig. II
• B. Fig. I and Fig. IV
• C. Fig. III and Fig. II
• D. Fig. III and Fig. IV

Hint:

In a series RC circuit, the charge on the capacitor increases exponentially while the current decreases exponentially.

Answer 1

The Correct Option is A

Step 1: Understanding capacitor charging in a series RC circuit.
When a capacitor is charged in a series RC circuit, the charge \(q(t)\) increases exponentially as the capacitor charges. The current \(i(t)\) decreases exponentially over time as the capacitor approaches full charge. The charge on the capacitor follows the equation: \[ q(t) = Q \left(1 - e^{-t/RC}\right) \] where \(Q\) is the maximum charge, and \(RC\) is the time constant.

Step 2: Analyzing the options.
- Fig. I and Fig. II: Fig. I shows the charge, which should increase over time, and Fig. II shows current, which should decrease over time. This matches the charging behavior of the capacitor.
- Fig. III and Fig. II: Fig. III shows a charge that decreases over time, which does not match the charging process. Therefore, this is the correct choice.

Step 3: Conclusion.
The correct answer is (C) Fig. III and Fig. II because Fig. III represents the increasing charge and Fig. II represents the exponentially decreasing current.