Question Detail
Question
A capacitor has a capacitance of 4.0 μF. The resistor has a resistance of 2.5 MΩ. Calculate the maximum value of the charging current and the charge stored by the capacitor when it is fully charged.
Correct Answer
Option A is the correct answer.
Detailed Explanation
Let's assume the charging voltage of the battery is V. 1. Maximum charging current (Imax) occurs at t=0 when the capacitor is uncharged and acts as a short circuit. Imax = V/R.2. When the capacitor is fully charged, the current stops flowing, and the voltage across the capacitor equals the battery voltage V. The maximum charge (Qmax) stored is Qmax = CV.By checking option A:If Imax = 4 μA = 4 × 10-6 A, then V = Imax * R = (4 × 10-6 A) * (2.5 × 106 Ω) = 10 V.If Qmax = 40 μC = 40 × 10-6 C, then V = Qmax / C = (40 × 10-6 C) / (4.0 × 10-6 F) = 10 V.Since both calculations yield V=10V, this option is consistent with an implied battery voltage of 10V.
Hint
Remember the formulas for maximum charging current (at t=0) and maximum charge stored (at t=infinity) in an RC circuit, assuming a charging voltage.