Question
In an oscillating $$LC$$ circuit with $$L = 50\,mH$$ and $$C = 4.0\,\mu F,$$ the current is initially a maximum. How long will it take before the capacitor is fully discharged for the first time :
A.
$$7 \times {10^{ - 4}}s$$
B.
$$14 \times {10^{ - 4}}s$$
C.
$$28 \times {10^{ - 4}}s$$
D.
none of these
Answer :
$$7 \times {10^{ - 4}}s$$
Solution :
Time period,
$$\eqalign{
& T = 2\pi \sqrt {LC} = 2\pi \sqrt {\left( {50 \times {{10}^{ - 3}}} \right) \times 4 \times {{10}^{ - 6}}} \cr
& = 28 \times {10^{ - 4}}\,s \cr} $$
Time taken by capacitor to charge fulley,
$$t = \frac{T}{4} = 7 \times {10^{ - 4}}s.$$