Ac Voltage Applied To A Series Lcr Circuit

Step 1: Understanding the Concept:
This question describes a series RLC circuit. The current in such a circuit is maximum when the circuit is in a state of resonance. Resonance occurs when the inductive reactance ( ) becomes equal to the capacitive reactance ( ), causing the total impedance of the circuit to be at its minimum value (equal to the resistance ).

Step 2: Key Formula or Approach:
The condition for resonance in a series RLC circuit is: where is the inductive reactance and is the capacitive reactance. By equating these, we get the formula for the resonant frequency, or we can solve for the capacitance needed for resonance at a given frequency .

Step 3: Detailed Explanation:
Given data:
Inductance, .
Frequency, .
Calculation:
Substitute the values into the formula for capacitance at resonance: Using the approximation : To express this value in microfarads (µF), we multiply by : This value is approximately 0.32 µF.

Step 4: Final Answer:
The required capacitance to achieve maximum current (resonance) is approximately 0.32 µF.