As the frequency of an ac circuit increases, the current first increases and then decreases. What combination of circuit elements is most likely to comprise the circuit ?

Options

A. Inductor and capacitor
B. Resistor and inductor
C. Resistor and capacitor
D. Resistor, inductor and capacitor.

Explanation

To determine the combination of circuit elements that causes the current in an AC circuit to first increase and then decrease as the frequency increases, we can analyze the behavior of different circuit components: resistors (R), capacitors (C), and inductors (L).

### Step-by-Step Solution:

1. **Understanding Impedance (Z)**:
- The total impedance (Z) in an AC circuit depends on the components present. For a circuit with a resistor (R) and a capacitor (C), the impedance is given by:
\[ Z = \sqrt{R^2 + (X_L - X_C)^2} \]
- Where \(X_L\) is the inductive reactance (\(X_L = \omega L\)) and \(X_C\) is the capacitive reactance (\(X_C = \frac{1}{\omega C}\)).

2. **Behavior of Reactance**:
- As frequency (f) increases, \(X_L\) increases linearly with frequency, while \(X_C\) decreases inversely with frequency.
- This means at low frequencies, \(X_C\) dominates, and at high frequencies, \(X_L\) dominates.

3. **Current Calculation**:
- The current (I) in the circuit can be expressed as:
\[ I = \frac{V_{rms}}{Z} \]
- Since \(V_{rms}\) is constant, the behavior of the current is inversely related to the impedance.

4. **Frequency Response**:
- At low frequencies, \(X_C\) is large, leading to a higher impedance and lower current.
- As frequency increases, \(X_C\) decreases, causing the impedance to decrease and the current to increase.
- Eventually, at very high frequencies, \(X_L\) becomes dominant, increasing the impedance again, which causes the current to decrease.

5. **Conclusion**:
- The combination of circuit elements that allows for this behavior (current first increasing and then decreasing with frequency) is a **combination of inductors and capacitors (RLC circuit)**. This is because the interplay between the inductive and capacitive reactance leads to a resonance effect, where the impedance is minimized at a certain frequency, allowing maximum current.

### Final Answer:
The most likely combination of circuit elements is **Inductor and Capacitor**.