How Can You Determine Inductance and Resistance in an LC Circuit?

In summary, a constant voltage at a frequency of 1MHz is maintained across a circuit consisting of an inductor in series with a variable capacitor. When the capacitor is set to 300pF, the current reaches its maximum value. By using the formula for the current in an RLC circuit, and with the knowledge that when the capacitor is reduced to 284pF the current is 0.707 times the maximum, we can find the inductance to be 337 microH. To find the resistance of the inductor, we can use the formula for the current and make it equal to 0.707 times the maximum current. By solving for R, we get a value of 2*pi*f*L -
  • #1
jayjay112
36
0
A constant voltage at a frequency of 1MHz is maintained across a circut consisting of the inductor in series with a variable capacitor. When the capacitor is set to 300pF the current has its max value. When the capacitor is reduced to 284pF the current is 0.707 of its ma value. Find

The inductance and the resistance of the inductor





Im not sure if I am using the correct formula.

f=[1/(2.pi)] x [1/(square root of (L).(C)]

f=frequency
L=Inductance
C=capacitance

L = 1/[(300x10^-12) x (2,000,000.pi)^2]

=337micro H

What formula could I use to find the resistance of the inductor?
 
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  • #2
use the second pair of info, and the formula for the current in an RLC circuit...
 
  • #3
Thaakisfox said:
use the second pair of info

What do you mean by use the second pair of info?

Thanks for your help
 
  • #4
well you know that when the capacity is 284pF then the current is 0.707 times the max...

So use the general formula for the current (containing R) and make it equal to 0.707 times the max current...
 
  • #5
Thaakisfox said:
well you know that when the capacity is 284pF then the current is 0.707 times the max...

So use the general formula for the current (containing R) and make it equal to 0.707 times the max current...

oh thanks,

so is the first part correct??
 
  • #6
yes that's cool...
 
  • #7
I = 0.707Imax when XL - XC = R
 
  • #8
rl.bhat said:
I = 0.707Imax when XL - XC = R


So i use this formula

I = V.R.C/L

I(max) = [V. R. (300x10^-12)] / (337x10^-6)

and then I = 0.707 I(max)

But i don't know V?
 
  • #9
Just calculate 2*pi*f*L -1/(2*pi*f*C). That is the value of R.
 

FAQ: How Can You Determine Inductance and Resistance in an LC Circuit?

What is electrical resonance?

Electrical resonance is a phenomenon that occurs when an electrical circuit or system is able to absorb and store energy at a specific frequency. This results in a large increase in the amplitude of the electrical current or voltage at that particular frequency.

How does electrical resonance work?

Electrical resonance works by using the principle of resonance, which is the tendency of a system to vibrate at its natural frequency when it is exposed to a periodic external force. In the case of electrical resonance, the external force is an alternating current or voltage at the resonant frequency of the circuit.

What are the applications of electrical resonance?

Electrical resonance has many practical applications, including in radio and television broadcasting, wireless communication systems, and electronic filters. Resonant circuits are also commonly used in electronic devices such as radios, amplifiers, and oscillators.

What factors affect electrical resonance?

The factors that affect electrical resonance include the inductance, capacitance, and resistance of the circuit. The resonant frequency of a circuit can be calculated using these parameters, and changing any one of them can alter the resonant frequency.

How can electrical resonance be controlled or avoided?

In order to control or avoid electrical resonance, engineers can design circuits with specific values of inductance, capacitance, and resistance that do not result in resonance. Additionally, adding damping elements such as resistors can help reduce the effects of resonance in a circuit.

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