Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
An LC circuit has H, and a resistance of . The capacitor starts with a charge of . Find the time in which the amplitude of the charge falls to half. Find the share of the starting energy that is left at that time. Find the number of oscillations in that time, using the frequency of the circuit without the resistance.
An LC circuit oscillates with , and . The charge is . The largest current is , and the total energy is . A resistance makes the amplitude fall as .
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. H, F and .
Step 1. The time. The amplitude falls to half when . Taking the natural logarithm, . We want , so s.
Step 2. The energy. The energy is proportional to the square of the charge amplitude. So it falls to , which is .
Step 3. The oscillations. Hz. In s there are oscillations.
Answer: s, and oscillations.
Check. The energy falls as . At s this is .
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