The amplitude of the charge oscillating in a circuit decreases exponentially as Q=Q_0 e^ -R t 2 L , 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 , L=12 mH , (2)=0.693 ]
B. 11.09 ms
Given Q=Q_0 e^ -R t / 2 L R=1.5 , L=12 mH , In (2)=0.693 Q=0.5 Q_0, t= ? 0.5 Q_0=Q_0 e^ -R t / 2 L 1 2 =e^ -R t / 2 L Taking log on both sides ( 1 2 )= e^ -R t / 2 L 2= R t 2 L t= 2 L In 2 R = 2 12 10^ -3 0.693 1.5 t=11.09 ~ms
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