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. (Assume a 10V battery is used for charging.)
Correct Answer
Option A is the correct answer.
Detailed Explanation
When a capacitor is fully charged in an RC circuit, the voltage across the capacitor equals the battery voltage (V). The charge (Q) stored is given by Q = CV.Q = (4.0 × 10⁻⁶ F) * (10 V) = 40 × 10⁻⁶ C = 40 μC.The maximum charging current (I_max) occurs at t=0 when the capacitor is uncharged and acts like a short circuit. At this moment, the entire battery voltage drops across the resistor. I_max = V/R.I_max = 10 V / (2.5 × 10⁶ Ω) = 4 × 10⁻⁶ A = 4 μA.Therefore, the maximum charging current is 4 μA and the charge stored when fully charged is 40 μC.
Hint
For a fully charged capacitor, Q=CV. Maximum charging current occurs at the very start (t=0) when the capacitor acts as a short circuit and I=V/R.