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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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