Question

Your latest invention is a car alarm that produces sound at a particularly annoying frequency of 3585 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 (the same voltage as the car battery). To produce a sufficiently loud sound, the capacitor must store 0.0163 J of energy. What values of capacitance and inductance should you choose for your car-alarm circuit?

Answer 1

Step-by-step explanation:

Energy stored in a capacitor = 1/2 C V² where , C is capacitance and V is potential of capacitor.

Putting the values

.5 x C x 12² = .0163

C = 226.4 x 10⁻⁶ F .

Frequency of L-C circuit =
`(1)/(2\pi)\sqrt{(1)/(LC) }`

where L is inductance of inductor and C is capacitance of capacitor.

putting the values

3585 =
`(1)/(2\pi)\sqrt{(1)/(L*226.4*10^(-6)) }`

506.87 x 10⁶ =
`(1)/(L*226.4*10^(-6))`

`L = (1)/(114755.37)`

= 8.7 x 10⁻⁶ H.