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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 12.0V . 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?

Short Answer

Expert verified

A) The value of capacitance is222μF

B) The value of inductance is9.31μH

Step by step solution

01

Concept of the energy in the capacitor

The energy in capacitor is Uc=12CV2where, C is the capacitance and V is the voltage

02

Calculate the values of capacitance

From the given value of the stored energy Uc in the capacitor, we can calculate the capacitance C

C=2UcV2=20.016J12V2=222×10-6F=222μF

Therefore, the value of capacitance is222μF

03

Calculate the values of inductance

For the self-inductance, we use the given value of frequency f from equation in the formL=12πf2C.Substitute the values in the given equation we get,

L=12π3500Hz2222μF=9.31μH

Therefore, the value of inductance is9.31μH

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Most popular questions from this chapter

A 140-g ball containing excess electrons is dropped into a 110-m vertical shaft. At the bottom of the shaft, the ball suddenly enters a uniform horizontal magnetic field that has magnitude 0.300 T and direction from east to west. If air resistance is negligibly small, find the magnitude ond direction of the force that this magnetic field exerts on the ball just as it enters the field.

Ordinary household electric lines in North America usually operate at 120 V . Why is this a desirable voltage, rather than a value considerably larger or smaller? On the other hand, automobiles usually have 12 V electrical systems. Why is this a desirable voltage?

If a “75-W” bulb (see Problem 25.35) is connected across a 220-V potential difference (as is used in Europe), how much power does it dissipate? Ignore the temperature dependence of the bulb’s resistance.


An electron at pointAinFig. E27.15has a speedv0of1.41×106m/sFind (a) the magnitude and direction of the magnetic field that will cause the electron to follow the semicircular path fromAtoB, and (b) the time required for the electron to move fromAtoB.

You connect a battery, resistor, and capacitor as in Fig. 26.20a, where R = 12.0 Ω and C = 5.00 x 10-6 F. The switch S is closed at t = 0. When the current in the circuit has a magnitude of 3.00 A, the charge on the capacitor is 40.0 x 10-6 C. (a) What is the emf of the battery? (b) At what time t after the switch is closed is the charge on the capacitor equal to 40.0 x 10-6 C? (c) When the current has magnitude 3.00 A, at what rate is energy being (i) stored in the capacitor, (ii) supplied by the battery

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