If frequency of alternating source is made zero then which of the following statement is true-

Options

A. current through capacitor will be zero
B. current through resistance will be zero
C. current through inductance will be zero
D. all

Answer

To solve the question, we need to analyze the behavior of current through a capacitor, resistor, and inductor when the frequency of the alternating source approaches zero.

### Step-by-Step Solution:

1. **Understanding the AC Source**:
The alternating source can be represented as:
\[ E = E_0 \sin(\omega t) \]
where \(\omega = 2\pi f\) and \(f\) is the frequency.

**Hint**: Remember that \(\omega\) is directly proportional to frequency \(f\).

2. **Current through the Inductor**:
The current through an inductor \(I_L\) is given by:
\[ I_L = \frac{E}{X_L} = \frac{E_0}{\omega L} \]
where \(X_L\) is the inductive reactance.

**Hint**: Reactance depends on frequency; as frequency approaches zero, observe what happens to \(X_L\).

3. **Current through the Capacitor**:
The current through a capacitor \(I_C\) is given by:
\[ I_C = \frac{E}{X_C} = E \cdot \omega C \]
where \(X_C = \frac{1}{\omega C}\) is the capacitive reactance.

**Hint**: Capacitive current is directly proportional to frequency; consider what happens when frequency is zero.

4. **Current through the Resistor**:
The current through a resistor \(I_R\) is given by:
\[ I_R = \frac{E}{R} \]
The resistance \(R\) does not depend on frequency.

**Hint**: Resistor current remains constant regardless of frequency changes.

5. **Setting Frequency to Zero**:
If the frequency \(f\) is made zero, then:
- \(\omega = 2\pi f = 0\)
- For the inductor:
\[ I_L = \frac{E_0}{0} \rightarrow \text{undefined (approaches infinity)} \]
- For the capacitor:
\[ I_C = E \cdot 0 = 0 \]
- For the resistor:
\[ I_R = \frac{E}{R} \text{ (remains finite)} \]

**Hint**: Analyze the implications of \(\omega\) being zero on each component.

6. **Conclusion**:
- Current through the capacitor \(I_C\) will be zero.
- Current through the resistor \(I_R\) will not be zero.
- Current through the inductor \(I_L\) will be undefined (or infinite).
- Therefore, the only true statement is that the current through the capacitor will be zero.

**Final Answer**: The correct option is **A**: Current through the capacitor will be zero.