Question

A soap bubble of radius r is charged to a potential V. If the radius is increased to n r, the potential on the bubble will become

• A. nV
  
• B. $n^{2}V$
  
• C. $\frac{V}{n}$
  
• D. $\frac{V}{n^2}$

Answer 1

The correct option is C $\frac{V}{n}$


If the radius of a bubble is increased by a factor n, its capacitance is also increased by a factor n, i.e. C'=nC. Since the charge Q on the bubble remains unchaged, we have
Q=CV=C' V'
or $V^{\prime }=\frac{CV}{C^{\prime }}=\frac{CV}{nC}=\frac{V}{n}$