Excess pressure in a soap bubble of radius r is proportional to:

Options

A. `1/r`
B. `1/(r^(2))`
C. r
D. `r^(2)`

Explanation

To find the relationship between excess pressure in a soap bubble and its radius, we can follow these steps:

### Step 1: Understand the Concept of Excess Pressure
Excess pressure in a soap bubble is the pressure difference between the inside and outside of the bubble. This excess pressure is influenced by the surface tension of the liquid forming the bubble and the radius of the bubble.

### Step 2: Use the Formula for Excess Pressure
The formula for the excess pressure (P) in a soap bubble is given by:

\[ P = \frac{4T}{R} \]

where:
- \( P \) is the excess pressure,
- \( T \) is the surface tension of the liquid,
- \( R \) is the radius of the bubble.

### Step 3: Analyze the Formula
In the formula \( P = \frac{4T}{R} \):
- The term \( 4T \) is a constant for a given soap solution, as the surface tension does not change.
- Therefore, we can see that the excess pressure \( P \) is inversely proportional to the radius \( R \).

### Step 4: Express the Proportionality
Since \( P \) is inversely proportional to \( R \), we can express this relationship as:

\[ P \propto \frac{1}{R} \]

This means that as the radius \( R \) of the soap bubble increases, the excess pressure \( P \) decreases.

### Conclusion
Thus, the excess pressure in a soap bubble of radius \( R \) is proportional to \( \frac{1}{R} \).

### Final Answer
The excess pressure in a soap bubble of radius \( R \) is proportional to \( \frac{1}{R} \).

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