Answered

Discover how IDNLearn.com can help you find the answers you need quickly and easily. Join our knowledgeable community and get detailed, reliable answers to all your questions.

The resistor in an RC circuit has a resistance of 200 Ω. The current decreases to 20% of its initial value in 2 ms. What is the value of the capacitance of the capacitor?

Sagot :

The capacitance of the capacitor is equal to 6.21*10^-6 F

Data;

  • Resistance = 200 Ω
  • Percentage decrease in current = 20%
  • time = 20ms = 20 * 10^-3

Capacitance of the Capacitor

The current in an RC circuit is given as

[tex]I = I_o e^-^\frac{t}{\tau}\\[/tex]

where τ represents the time constant of circuit.

At t = 2.0*10^-3s

[tex]0.2I_o = I_o e ^ - ^ \frac{2*10^-^3}{\tau}\\e ^\frac{2.0*10^-^3}{\tau} = \frac{1}{0.2} =5\\ \frac{2*10^-^3}{\tau} = \ln5\\ \tau = \frac{2.0*10^-^3}{\ln5}= RC = \frac{2.0*10^-^3}{\ln5}\\ c = \frac{2.0*10^-^3}{200\ln5} \\ c= 6.21*10^-^6F[/tex]

The capacitance of the capacitor is equal to 6.21*10^-6 F

Learn more on capacitance in an RC circuit here;

https://brainly.com/question/14883923

https://brainly.com/question/15183130

Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. Your search for solutions ends here at IDNLearn.com. Thank you for visiting, and come back soon for more helpful information.