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Physics / Sears and Zemansky's University Physics with Modern Physics 13 / Chapter 30 / Problem 57P

Sears and Zemansky's University Physics with Modern Physics | 13th Edition | ISBN: 9780321696861 | Authors: Hugh D. Young; Roger A. Freedman; A. Lewis Ford

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Chapter 30, Problem 57P

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QUESTION:

Problem 57P

An Electromagnetic Car Alarm. Your latest invention is a car alarm that produces sound at a particularly annoying frequency of 3500 Hz. To do this, the car-alarm circuitry must produce an alternating electric current of the same frequency. That’s why your design includes an inductor and a capacitor in series. The maximum voltage across the capacitor is to be 12.0 V. To produce a sufficiently loud sound, the capacitor must store 0.0160 J of energy. What values of capacitance and inductance should you choose for your car-alarm circuit?

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QUESTION:

Problem 57P

An Electromagnetic Car Alarm. Your latest invention is a car alarm that produces sound at a particularly annoying frequency of 3500 Hz. To do this, the car-alarm circuitry must produce an alternating electric current of the same frequency. That’s why your design includes an inductor and a capacitor in series. The maximum voltage across the capacitor is to be 12.0 V. To produce a sufficiently loud sound, the capacitor must store 0.0160 J of energy. What values of capacitance and inductance should you choose for your car-alarm circuit?

ANSWER:

Step 1 of 2

$Given\ \ \ \ \ \ \ \ \ \$

$\ \ U=0.0160\ J\$

$\ V\ =12\ V$

$\ \ C=?\$

$\ \ f=3500\ Hz$

$\ \ \ \ L=?$

$The\ energy\ stored\ in\ the\ capacitor\ is\ U=\frac{1}{2}\ C{V}^{2}$

$Now\ we\ have\ to\ find\ the\ capacitance\ C,$

$C=\frac{2U}{{V}^{2}}=\frac{2\times{}0.0160\ J}{(12\ V{)}^{2}}=222\times{}{10}^{-6}F=222\ \mu{}F$

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