SATHEE: Electro Magnetic Induction And Alternating Currents Question 186

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:

$i_{1} = \frac{d q}{d t} = \frac{d}{d t} (2 \cos 4 t) = - 8 \sin 4 t$ ,

$i_{2} = \frac{d q}{d t} = \frac{d}{d t} (4 \cos t) = - 4 \sin t$ ,

$i_{3} = \frac{d q}{d t} = \frac{d}{d t} (3 \cos 4 t) = - 12 \sin 4 t$ ,

$i_{4} = \frac{d q}{d t} = \frac{d (4 \cos 2 t)}{d t} = - 8 \sin 2 t$

Clearly, amplitude of $i_{3}$ is greatest.

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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:

Answer:

Solution:

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