2024 Re-NEET Alternating CurrentDamped LC oscillations - charge decay Medium Question 9 of 60 in Alternating Current

The amplitude of the charge oscillating in a circuit decreases exponentially as $Q=Q_0e^{-Rt/2L}$, where $Q_0$ is the charge at $t=0$ s. The time at which charge amplitude decreases to $0.50\,Q_0$ is nearly: [Given that $R=1.5\ \Omega$, $L=12$ mH, $\ln(2)=0.693$]

A 19.01 ms
B 11.09 ms
C 19.01 s
D 11.09 s

The answer is B.

Solution

$0.5Q_0=Q_0e^{-Rt/2L}\Rightarrow\dfrac{1}{2}=e^{-Rt/2L}$. Taking natural log: $\ln2=\dfrac{Rt}{2L}\Rightarrow t=\dfrac{2L\ln2}{R}=\dfrac{2\times12\times10^{-3}\times0.693}{1.5}=11.09$ ms.

Concept Damped LC oscillations - charge decay

Alternating Current in past papers

60 questions from this chapter have appeared across 24 exam years.