In a series RLC circuit, if the frequency is increased to a very large value, what value does the phase angle between current and voltage approach ?

Options

A. `90^(@)`
B. `0^(@)`
C. `30^(@)`
D. `45^(@)`

Answer

To solve the problem of finding the phase angle between current and voltage in a series RLC circuit as the frequency approaches a very large value, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Components**: In a series RLC circuit, we have a resistor (R), an inductor (L), and a capacitor (C). The behavior of the circuit changes with frequency.

2. **Identify Reactances**: The capacitive reactance (Xc) and inductive reactance (Xl) are given by:
- \( X_c = \frac{1}{\omega C} \)
- \( X_l = \omega L \)
where \( \omega = 2\pi f \) (angular frequency).

3. **Analyze Reactances at High Frequency**:
- As the frequency \( f \) increases to a very large value, \( \omega \) approaches infinity.
- Therefore, \( X_c \) approaches 0 (since \( X_c = \frac{1}{\omega C} \)).
- Conversely, \( X_l \) approaches infinity (since \( X_l = \omega L \)).

4. **Determine Phase Angle**: The phase angle \( \phi \) between the current and voltage in an RLC circuit can be determined using the relationship:
\[ \tan \phi = \frac{X_l - X_c}{R} \]
Since \( X_c \) approaches 0 and \( X_l \) approaches infinity, we have:
\[ \tan \phi = \frac{\infty - 0}{R} = \frac{\infty}{R} = \infty \]

5. **Conclude the Phase Angle**: When \( \tan \phi \) approaches infinity, the phase angle \( \phi \) approaches \( 90^\circ \). Thus, the phase angle between the current and voltage approaches:
\[ \phi = 90^\circ \]

### Final Answer:
The phase angle between current and voltage in a series RLC circuit approaches \( 90^\circ \) as the frequency is increased to a very large value.

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