If the plates of a capacitor are joined together by as conducting wire, then its capacitance

Options

A. reamains unchanged
B. decreases
C. become zero
D. becomes infinite

Explanation

To solve the problem of what happens to the capacitance of a capacitor when its plates are joined together by a conducting wire, we can follow these steps:

### Step 1: Understand the Definition of Capacitance
Capacitance (C) is defined as the ability of a system to store charge per unit voltage. Mathematically, it is given by the formula:
\[ C = \frac{Q}{V} \]
where:
- \( C \) is the capacitance,
- \( Q \) is the charge stored on the plates,
- \( V \) is the potential difference between the plates.

### Step 2: Analyze the Effect of Joining the Plates
When the plates of the capacitor are joined together by a conducting wire, they effectively become a single conductor. This means that the potential difference (V) between the plates becomes zero because both plates are at the same electric potential.

### Step 3: Substitute into the Capacitance Formula
Since the potential difference \( V \) is now zero, we can substitute this into the capacitance formula:
\[ C = \frac{Q}{0} \]
This expression implies that capacitance approaches infinity because dividing by zero is undefined in mathematics.

### Step 4: Conclusion
Thus, when the plates of a capacitor are joined together by a conducting wire, the capacitance approaches infinity. This is because the distance between the plates effectively becomes zero, allowing for an infinite amount of charge to be stored for any finite voltage.

### Final Answer
The capacitance of the capacitor approaches infinity.

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