A variable capacitor is connected to an ac source. What effect does decreasing the capacitance have on the reactance and current in this circuit?

Options

A. Reactance - No change , Current - No change
B. Reactance - Decreases , Current - No change
C. Reactance - Increases , Current - Increases
D. Reactance - Increases , Current - Decreases

Answer

To solve the question regarding the effect of decreasing the capacitance on the reactance and current in a circuit with a variable capacitor connected to an AC source, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between capacitance, reactance, and current:**
- The reactance \( X_c \) of a capacitor in an AC circuit is given by the formula:
\[ X_c = \frac{1}{2 \pi f C} \]
where \( f \) is the frequency of the AC source and \( C \) is the capacitance.

2. **Analyze the effect of decreasing capacitance:**
- If the capacitance \( C \) is decreased, we can observe the effect on reactance \( X_c \).
- Since \( X_c \) is inversely proportional to \( C \), decreasing \( C \) will lead to an increase in \( X_c \):
\[ \text{If } C \downarrow \Rightarrow X_c \uparrow \]

3. **Determine the relationship between reactance and current:**
- The current \( I \) in the circuit is related to the reactance by Ohm's law, where:
\[ I = \frac{V}{X_c} \]
where \( V \) is the voltage of the AC source.
- Since \( X_c \) increases when \( C \) decreases, the current \( I \) will decrease:
\[ \text{If } X_c \uparrow \Rightarrow I \downarrow \]

4. **Summarize the findings:**
- Therefore, when the capacitance is decreased, the reactance increases and the current decreases.

5. **Conclude with the correct option:**
- Based on the analysis, the correct conclusion is that decreasing the capacitance results in an increase in reactance and a decrease in current.

### Final Answer:
- **Reactance increases and current decreases.**

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