In an alternating current circuit consisting of elements in series, the current increases on increasing the frequency of supply. Which of the following elements are likely to constitute the circuit ?

Options

A. only resistor
B. Resistor and an inductor
C. Resistor and capacitor
D. Only a capacitor

Explanation

To solve the problem, we need to analyze the behavior of an alternating current (AC) circuit consisting of various elements in series, particularly focusing on how the current changes with frequency.

### Step-by-Step Solution:

1. **Understanding the Relationship**:
- The current \( I \) in an AC circuit can be expressed using Ohm's law as:
\[ I = \frac{V}{Z} \]
where \( V \) is the voltage and \( Z \) is the impedance of the circuit.

2. **Impedance in an LCR Circuit**:
- The impedance \( Z \) in a series LCR circuit is given by:
\[ Z = \sqrt{R^2 + (X_L - X_C)^2} \]
where \( X_L \) is the inductive reactance and \( X_C \) is the capacitive reactance.

3. **Reactance Definitions**:
- The inductive reactance \( X_L \) is defined as:
\[ X_L = \omega L = 2 \pi f L \]
- The capacitive reactance \( X_C \) is defined as:
\[ X_C = \frac{1}{\omega C} = \frac{1}{2 \pi f C} \]

4. **Frequency Dependency**:
- From the definitions, we see that:
- \( X_L \) increases with increasing frequency \( f \).
- \( X_C \) decreases with increasing frequency \( f \).

5. **Analyzing the Given Condition**:
- The problem states that the current increases as the frequency increases. This implies that the impedance \( Z \) must decrease because \( I \) is inversely proportional to \( Z \).

6. **Implications for Circuit Elements**:
- If \( Z \) decreases with increasing frequency, it suggests that:
- The contribution of \( X_L \) (inductive reactance) must not dominate since it would increase \( Z \).
- The contribution of \( X_C \) (capacitive reactance) must dominate since it decreases with increasing frequency.

7. **Conclusion on Circuit Elements**:
- Since inductance increases with frequency, it cannot be present in the circuit if the current is to increase. Thus, we can conclude that:
- The circuit cannot consist of an inductor.
- The circuit can consist of a capacitor or a combination of a resistor and a capacitor.

8. **Final Answer**:
- Therefore, the elements likely to constitute the circuit are:
- Only a capacitor or a resistor and a capacitor in series.