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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

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