Question

You measure the capacitor and inductor voltages in a driven RLC circuit, and find 10V for the rms capacitor voltage and 15V for the rms inductor voltage.

• A. $\omega ={\omega }_{res}$
• B. $\omega <{\omega }_{res}$
• C. $\omega >{\omega }_{res}$
• D. Can't be said

Answer 1

The correct option is C $\omega >{\omega }_{res}$

A/c to ques $V_c=10V$ and $V_2=15V$

Let frequency be $W$ capacitance be $C$ and inductance be $L$

$\Rightarrow i{X}_C=10$ and $i{X}_L=15$

$\Rightarrow \frac{i}{WL}=10$ and $i\left(WL\right)=15$

Dividing both

$\frac{\frac{i}{WC}}{iVWL}=\frac{10}{15}$

$\Rightarrow W^2=\frac{3/2}{LC}$

$W=\frac{\sqrt{1.5}}{\sqrt{LC}}$

we know that $W_{resonance}=\frac{1}{\sqrt{LC}}....\left(2\right)$

Clearly from $\left(1\right)$ and $\left(2\right)$ $W>W_{res}\left(C\right)$