Browse by Stream
Discuss Doubts
Home
Search for Exam, Articles, Questions
get app
Go To Your Study Dashboard
  1. Home
  2. An LC circuit contains a 20 mH inductor and a 50 μF capacitor with an initial charge of 10 mC. The resistance of the circuit. what times is the total energy shared

Filters

Select Stream
Select Type
Select Exam
Select Subject
Select Chapter
Select Exercise
Q&A - Ask Doubts and Get Answers
Q
NCERT

An LC circuit contains a 20 mH inductor and a 50 μF capacitor with an initial charge of 10 mC. The resistance of the circuit. what times is the total energy shared

Q7.12 (d)    An LC circuit contains a 20mH inductor and a 50\mu F capacitor with an initial charge of 10mC. The resistance of the circuit is negligible. Let the instant the circuit is closed be t=0.

At what times is the total energy shared equally between the inductor and the capacitor?

 

Answers (1)
Views
P Pankaj Sanodiya

The energy will be shared equally when the energy in the capacitor is half of the maximum energy it can store.i.e.

\frac{Q^2}{2C}=\frac{1}{2}\frac{Q_0^2}{2C}

From Here, we got

Q=\frac{Q_0}{\sqrt{2}}

So Now, we know the charge on the capacitor, we can calculate time for which

\frac{Q_0}{\sqrt{2}}=Q_0cos\left ( \frac{2\pi t}{T} \right )

\frac{1}{\sqrt{2}}=cos\left ( \frac{2\pi t}{T} \right )

From here,

 t=\frac{T}{8},\frac{3T}{8},\frac{5T}{8}..

Hence for these times, the total energy will be shared equally between capacitor and inductor. 

Similar Questions

Related Chapters

Exams
Articles
Questions