Question

An $\text{AC}$ generator $G$ with an adjustable frequency of oscillation is used in the circuit, as shown .

• A.
  Current from source is maximum if angular frequency is $5000\text{rad/sec}$
• B.
  Themal energy produced by $R$ in $1\mu \text{s}$ is $100\mu \text{J}$
• C.
  Average energy stored by inductor $L_2$ is $1.2\text{mJ}$
• D.
  If $C_3$ is removed resonance frequency will increase.

Answer 1

Answer: (A), (C), (D)

If $C_3$ is removed resonance frequency will increase.
Current drawn is maximum at resonant angular frequency,

$L_{eq}=4\text{mH};C_{eq}=10\mu \text{F}$

$\omega =\frac{1}{\sqrt{LC}}=5000\text{rad/s}$

As $1\mu \text{s}$ time duration is very less than time period $T$ at resonance, thermal energy produced is not possible to calculate without information about start of the given time duration. (Option B wrong.)

Average energy stored $=\frac{1}{2}L{i}_{rms}^2=\frac{1}{2}(2.4\times {10}^{-3})\times (1{)}^2=1.2\text{mJ}$

Option C correct

When $C_3$ is removed, $C_{eq}$ decreases thereby increasing resonant frequency.

Option D correct.