1. Pressure inside a soap bubble

For a soap bubble of radius $R$, the excess pressure inside it is

$\Delta P = \frac{4T}{R}$

where $T$ is the surface tension.

So the pressure inside the bubble is

$P_{\text{inside}} = P_{\text{outside}} + \frac{4T}{R}$

2. Compare the pressures of two bubbles

Let the radii of the two bubbles be $R_1$ and $R_2$, with

$R_1 < R_2$

Then their excess pressures are

$\Delta P_1 = \frac{4T}{R_1}, \qquad \Delta P_2 = \frac{4T}{R_2}$

Since $R_1 < R_2$,

$\frac{4T}{R_1} > \frac{4T}{R_2}$

Hence,

$P_1 > P_2$

So the smaller bubble has higher internal pressure than the bigger bubble.

3. Direction of air flow

When the two bubbles are connected by a tube, air flows from higher pressure to lower pressure.

Therefore, air flows:

$\text{smaller bubble} \to \text{bigger bubble}$

4. Check options

• A: air flows from the smaller bubble to the bigger ✅
• B: air flows from bigger bubble to the smaller bubble till the sizes are interchanged ❌
• C: air flows from the bigger bubble to the smaller bubble till the sizes become equal ❌
• D: there is no flow of air ❌

5. Final answer

The correct option is:

$\boxed{\text{A}}$