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Q10P

Expert-verifiedFound in: Page 936

Book edition
10th Edition

Author(s)
David Halliday

Pages
1328 pages

ISBN
9781118230718

**LC ****oscillators have been used in circuits connected to loudspeakers to create some of the sounds of electronic music. What inductance must be used with a 6.7 µF capacitor to produce a frequency of 10 kHz****, which is near the middle of the audible range of frequencies?**

The inductance to be used is $3.78\times {10}^{-5}\text{H}$ , which is near the middle of the audible range of frequencies.

- The capacitance of the capacitor, $C=6.7\mathrm{\mu F}$.
- The frequency that the capacitor will produce $f=10\text{kHz or}10000\text{Hz}$.

**Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. By using the direct relationship between the frequency of inductance and the inductance, we can find the inductance.**

Formulae:

The resonance frequency of an LC oscillation, $f=\frac{1}{2\pi \sqrt{LC}}$. (i)

By using equation (i), we can find the inductance to be used having frequency near the middle of the audible range of frequencies as follows:

$\begin{array}{rcl}L& =& \frac{1}{{\left(2\pi \right)}^{2}{f}^{2}C}\\ & =& \frac{1}{{\left(2\pi \right)}^{2}{10000}^{2}\times 6.7\times {10}^{-6}}\\ & =& \frac{1}{{\left(2\pi \right)}^{2}{10000}^{2}\times 6.7\times {10}^{-6}}\\ & =& 3.78\times {10}^{-5}\text{H}\\ & & \end{array}$

Hence, the value of the inductance is $3.78\times {10}^{-5}\text{H}$.

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