1. Concept used: Excess pressure due to surface tension

For a curved liquid surface, pressure inside is greater than pressure outside due to surface tension.

• For a liquid drop (one surface): $\Delta P = \frac{2S}{R}$
• For a soap bubble (two surfaces: inner and outer): $\Delta P = 2\times \frac{2S}{R} = \frac{4S}{R}$

2. Apply to the soap bubble

Given:

• Radius of bubble $= R$
• Surface tension $= S$

Therefore, excess pressure inside the soap bubble is $P_{\text{inside}} - P_{\text{outside}} = \frac{4S}{R}$

3. Check options

• A: $\frac{S}{R}$ ❌
• B: $\frac{4S}{R}$ ✅
• C: $\frac{4R}{S}$ ❌ (dimensionally wrong)
• D: $\frac{2S}{R}$ ❌ (this is for a liquid drop, not a soap bubble)

Hence, the correct option is B.