Question

For your final exam in electronics, you’re asked to build an LC circuit that oscillates at 10 kHz. In addition, the maximum current must be 0.10 A and the maximum energy stored in the capacitor must be 1.0 x 10-5 J. What values of inductance and capacitance must you use?

Answer 1

L= 2 mH

`C=1.26* 10^(-7)\ F`

Step-by-step explanation:

Given that

Frequency , f= 10 kHz

Maximum current ,I = 0.1 A

Maximum energy stored ,E= 1 x 10⁻⁵ J

The maximum energy stored in the inductor is given as follows

`E=(1)/(2)LI^2`

Where ,L= Inductance

I=Current

E=Energy

Now by putting the values in the above equation

`10^(-5)=(1)/(2)* L* 0.1^2`

`L=(2* 10^(-5))/(0.1^2)\ H`

L=0.002 H

L= 2 mH

We know that frequency f is given as

`2\pi f=(1)/(√(LC))`

C=Capacitance , f=frequency ,L=Inductance

Now by putting the values

`2\pi * 10* 10^3=(1)/(√(0.002* C) )`

`62831.85=(1)/(√(0.002* C))`

`\sqrt{0.002* C=(1)/(62831.85)`

`0.002* C=0.0000159^2`

`C=(0.0000159^2)/(0.002)\ F`

`C=1.26* 10^(-7)\ F`

Therefore the inductance and capacitance will be 2 mH and 1.26 x 10⁻⁷ F respectively.

Answer 2

Given the following data:

Frequency = 10 kHz

Maximum current = 0.10 Amps

Maximum energy =
`1.0 * 10^(-5)` Joules

To find the values of inductance and capacitance that must be used for this LC circuit:

For the inductance:

Mathematically, the maximum energy stored in an inductor is given by the formula:

`E = (1)/(2) LI^2`