What is the ratio of $V _ { \mathrm { OUT } } / V _ { \mathrm { IN } }$ (expressed in dB ) in an RLC series resonant circuit if the output voltage is taken across the inductor, the resonant frequency is 14 MHz , the source voltage is 18 V and the inductor drops 300 V ?
A) 28 dB
B) 24.4 dB
C) 14.0 dB
D) 42.9 dB

Question

What is the ratio of $V _ { \mathrm { OUT } } / V _ { \mathrm { IN } }$ (expressed in  dB ) in an RLC series resonant circuit if the output voltage is taken across the inductor, the resonant frequency is  14 MHz , the source voltage is  18 V  and the inductor drops  300 V ?
A)  28 dB
B)  24.4 dB
C)  14.0 dB
D)  42.9 dB

Quizplus · Accepted Answer

We know that for an RLC circuit, the resonant frequency is given by:

$$f = \frac{1}{2\pi\sqrt{LC}}$$

Substituting with the given values:

$$14 	imes 10^6 = \frac{1}{2\pi\sqrt{L	imes 10^{-8}	ext{ F} 	imes C	imes10^{-12}	ext{ F}}}$$

Simplifying, we get:

$$L = 20.69 	ext{ }\mu	ext{H}$$

Now, the voltage across the inductor is given as 300 V and the source voltage is given as 18 V. Therefore, the voltage gain (or the ratio of output voltage to input voltage) is:

$$\frac{V_{	ext{out}}}{V_{	ext{in}}} = \frac{V_L}{V_{	ext{in}}} = \frac{300	ext{ V}}{18	ext{ V}} = 16.67$$

Taking the ratio in decibels:

$$	ext{Gain (in dB)} = 20 \log \left(\frac{V_{	ext{out}}}{V_{	ext{in}}}ight) = 20 \log(16.67) \approx \boxed{24.4	ext{ dB}}$$

Therefore, the answer is B.

What Is the Ratio Of VOUT/VINV _ { \mathrm { OUT } } / V _ { \mathrm { IN } }VOUT​/VIN​

What Is the Ratio Of $V _ { \mathrm { OUT } } / V _ { \mathrm { IN } }$