Question

An air filled parallel plate capacitor charged to potential $ {{V}_{1}} $ is connected to an uncharged identical parallel plate capacitor with dielectric constant K. The common potential is $ {{V}_{2}} $ . The value of K is

• A. $ \frac{{{V}_{1}}-{{V}_{2}}}{{{V}_{1}}+{{V}_{2}}} $
• B. $ \frac{{{V}_{1}}}{{{V}_{1}}-{{V}_{2}}} $
• C. $ \frac{{{V}_{1}}-{{V}_{2}}}{{{V}_{2}}} $
• D. $ \frac{{{V}_{1}}-{{V}_{2}}}{{{V}_{1}}} $

Answer 1

Answer: (C)

Common potential $ =\frac{total\text{ }charge}{total\text{ }capacity} $ $ {{V}_{2}}=\frac{{{C}_{0}}{{V}_{1}}+0}{{{C}_{0}}+K{{C}_{0}}}=\frac{{{V}_{1}}}{1+K} $ $ 1+K=\frac{{{V}_{1}}}{{{V}_{2}}} $ $ K=\frac{{{V}_{1}}-{{V}_{2}}}{{{V}_{2}}} $