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A resistor with resistance 10MOmega is c...

A resistor with resistance `10MOmega` is connected in series with a capacitot of capcitance `1.0muF` and a battery with emf 12.0V, Before the switch is closed at time t= 0 the capacitor is uncharged.
a. What is the time constant?
b. What fraction of the final charge is on the plates at tiem t = 46s?
c. kWhat fraction of the inital current remians at t =46?

Text Solution

Verified by Experts

a. The time constant is `tau = RC = 10xx10^6xx1xx10^(-6) = 10s`
b. The fraction f of the final charge on capacitor is `q//Q`
`(q)/(Q) = 1-e^(-t//RC) = 1-e^(-46//10) = 0.99`
The capacitor is 99% charged after a tiem equal to
4.6 RC, or 4.6 time constants.
c. `(I)/(I_0) = e^(-4.6) = 0.10`
After 4.6 time constant, the current has decreased to
1.0% of its inital value.
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