Question

In an a.c. circuit with pure capacitance 'C' and a.c. source \(E = E_0sinωt\), the equation of instantaneous current is given by

• A. \(I = E_0\,ωC\cdot sin(ωt)\)
• B. \(I = E_0ωCsin(ωt+\frac{π}{2})\)
• C. \(I = \frac{E_0}{ωC}sin(ωt)\)
• D. \(I = \frac{E_0}{ωC}sin(ωt+\frac{π}{2})\)

Hint:

Resonant frequency is 1 over 2 pi root LC.

Answer 1

The Correct Option is B

Step 1: Scaling law:
$f\propto\frac{1}{\sqrt{LC}}$. Multiplying the product $LC$ by a factor k divides f by $\sqrt k$.

Step 2: Factor:
$LC$ becomes $3L\cdot9C = 27\,LC$, so $k = 27$ and $f' = \frac{f}{\sqrt{27}} = \frac{f}{3\sqrt3}$ (D).

Final Answer:
$\frac{f}{3\sqrt3}$. \[ \boxed{\frac{f}{3\sqrt{3}}} \]