Electro Magnetic Induction And Alternating Currents Question 186
Question: Charges on the capacitors in four oscillating LC circuits vary as follows: (1) q=2 cos 4t, (2) q =4 cos t, (3) q = 3 cos 4t, (4) q = 4 cos 2t, with q in coulomb and t in second. In which circuit(s) current amplitude is greatest?
Options:
A) (1)
B) (2)
C) (3)
D) (4)
Show Answer
Answer:
Correct Answer: C
Solution:
-
$ i _{1}=\frac{dq}{dt}=\frac{d}{dt}(2\cos 4t)=-8\sin 4t $ ,
$ i _{2}=\frac{dq}{dt}=\frac{d}{dt}(4\cos t)=-4\sin t $ ,
$ i _{3}=\frac{dq}{dt}=\frac{d}{dt}(3\cos 4t)=-12\sin 4t $ ,
$ i _{4}=\frac{dq}{dt}=\frac{d(4\cos 2t)}{dt}=-8\sin 2t $
Clearly, amplitude of $ i _{3} $ is greatest.
