A parallel-plate capacitor has plates of unequal area . The larger plates is connected to the positive terminal of the battery and the smaller plate to its nagative terminal. Let Q+ and Q-be the charges appearing on the positive and negative plates respectively

Options

A. `Q_+gtQ-`
B. `Q_=Q-`
C. `Q_+ltQ-`
D. The information is not sufficient to decide the ralation between `Q_+` and `Q_.`

Answer

To solve the problem regarding the charges on the plates of a parallel-plate capacitor with unequal areas, we will follow these steps:

### Step 1: Understand the Configuration
We have a parallel-plate capacitor with two plates of unequal area. The larger plate is connected to the positive terminal of a battery, while the smaller plate is connected to the negative terminal.

**Hint:** Visualize the capacitor setup and identify which plate is connected to which terminal of the battery.

### Step 2: Identify the Charges
When a capacitor is connected to a battery, the plate connected to the positive terminal accumulates a positive charge (Q+) and the plate connected to the negative terminal accumulates a negative charge (Q-).

**Hint:** Remember that the convention is that the positive charge appears on the plate connected to the positive terminal.

### Step 3: Relate Charge to Voltage
The relationship between the charge (Q) on the plates of a capacitor and the voltage (V) across the capacitor is given by the equation:
\[ Q = C \cdot V \]
where C is the capacitance of the capacitor.

**Hint:** Capacitance (C) is a property of the capacitor and does not depend on the area of the plates in this context.

### Step 4: Analyze the Capacitance
For a parallel-plate capacitor, the capacitance is given by:
\[ C = \frac{\varepsilon_0 \cdot A}{d} \]
where \( \varepsilon_0 \) is the permittivity of free space, \( A \) is the area of the plates, and \( d \) is the distance between the plates. However, this does not affect the relationship between the charges on the plates.

**Hint:** Focus on the fact that the capacitance relates to the geometry of the plates but does not change the fundamental charge relationship.

### Step 5: Conclude the Relationship Between Charges
Since the charges on the plates of a capacitor are equal in magnitude but opposite in sign, we can state:
\[ |Q+| = |Q-| \]
This means that the positive charge on the larger plate (Q+) is equal in magnitude to the negative charge on the smaller plate (Q-).

**Hint:** Remember that in a capacitor, the total charge is conserved, leading to the conclusion that the magnitudes of the charges are equal.

### Final Answer
Thus, we conclude that:
\[ Q+ = Q- \]

The correct option is:
**Option 2: Q+ is equal to Q-.**