time elapsed before the amplitude of the oscillations drops to half its initial value = 6.915 ms .
A resistor (R), an inductor (L), and a capacitor (C) coupled either in series or parallel make up an RLC circuit. The letters used to identify the circuit's constituent parts—where the order of the parts may differ from RLC—were utilized to create the circuit's name.
The circuit echoes like an LC circuit and creates a harmonic oscillator for current. The addition of the resistor accelerates the oscillations' decline, sometimes referred to as damping. The highest resonant frequency is likewise decreased by the resistor. Even though a resistor is not officially mentioned as a component, some resistance is unavoidable.
l = 10 mh c = 1.5 f r = 2.0
amplitude of charge oscillation = q[tex]e^{-bt}[/tex]
we have [tex]e^{-bt}[/tex] = 1/2
t = ln 2 / b
= (ln 2) * 2l / r
=(ln 2) * 2 * 10 * [tex]10^{-3}[/tex] / 2
= 6.9315 ms .
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