Question

In an oscillating LC circuit the maximum charge on the capacitor is $ Q. $ The charge on the capacitor when the energy is stored equally between the electric and magnetic fields is

• A. $ Q/2 $
• B. $ Q/\sqrt{3} $
• C. $ Q/\sqrt{2} $
• D. $ Q $

Answer 1

Answer: (C)

In an $ LC $ circuit the energy oscillates between inductor (in the magnetic field) and capacitor (in the electric field). $ {{U}_{E\,\,\max }} $ [Maximum energy stored in capacitor] $ =\frac{{{Q}^{2}}}{2C} $ $ {{U}_{B\,\,\max }} $ [Maximum energy stored in inductor] $ =\frac{Li_{0}^{2}}{2} $ where $ {{I}_{0}} $ is the current at this time. For the given instant $ {{U}_{E}}={{U}_{B}} $ $ ie, $ $ \frac{{{q}^{2}}}{2C}=\frac{L{{i}^{2}}}{2} $ From energy conservation $ {{U}_{E}}+{{U}_{B}}={{U}_{E\,\,\max }}={{U}_{B\,\,\max }} $ $ \Rightarrow $ $ 2\frac{{{q}^{2}}}{2C}=\frac{{{Q}^{2}}}{2C} $ $ \Rightarrow $ $ q=\frac{Q}{\sqrt{2}} $