Question

What is the resonance frequency of a series RLC circuit where R=10Ω, L= 25mH and C= 100uF.

Evalute Q factor also. ​

Answer 1

Answer:

Resonance Frequency: 632.5 Hz

Q Factor: 1.58

Explanation:

Given:

• Resistance (r) = 10Ω
• Inductance (l) = 25mH
• Conductance (c) = 100uF

To find:

• Resonance Frequency (wo)
• Q (Quality) Factor (q)

Solution:

Resonant frequency for a series RLC circuit is given by:

$resonant \: frequency \: \frac{1}{ \sqrt{inductance \: \times \: conductance} }$

$wo \: = \: \frac{1}{ \sqrt{lc} }$

On putting the values, we get

$wo \: = \: \frac{1}{ \sqrt{25 \times {10}^{ - 3} \: \times 100 \times {10}^{ - 6} } }$

$wo \: = \: 632.5$

Therefore, resonant frequency (wo) is 632.5 Hz.

Now,

Bandwidth for a series RLC circuit is given by:

$bandwidth \: = \frac{resistance}{inductance}$

$b \: = \frac{r}{l}$

On putting the values, we get

$b \: = \: \frac{10}{25 \times {10}^{ - 3} } = 400$

Therefore, the value of bandwidth (b) is 400.

Now,

The quality (Q) factor is given by:

$quality \: factor = \frac{resonant \: frequency}{bandwidth}$

$q \: = \frac{wo}{b}$

On putting the values, we get

$q \: = \: \frac{632.5}{400} = 1.58$

Therefore, the value of Quality Factor (q) is 1.58.

Formula Used:

Resonant Frequency:

• $wo \: = \: \frac{1}{ \sqrt{lc} }$

Bandwidth:

• $b \: = \frac{r}{l}$

Q Factor:

• $q \: = \frac{wo}{b}$

For more similar reference:

https://brainly.in/question/16697849

https://brainly.in/question/21170723

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