Question:

Anyone help me with this physics problem? :)

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A 2.0 F capacitor is charged to 11.0 V . It is then connected across a 500 kOmega resistor.

(1).How long does it take for the capacitor voltage to reach 5.0 V ?

(2).How long does it take for the energy stored in the capacitor to decrease to half its initial value?

Thank you!

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  1. voltage is subject to equation:

    V(t) =V0*exp(-t/(RC)), where C=2.0F, R=500e3 Ohm, V0=11.0 volts;    

    ♦Thus 5 = 11*exp(-t/(CR)); or; ln(5/11) = -t/(2*500e3), hence

    t=2*5e5*ln(11/5) =788457.4s ≈ 9days 3 hours;

    ♦ E(t)=0.5*C*V(t)^2;

    (0.5*C*V0^2)/2 = 0.5C* V0^2*exp(-2*t/(RC));

    0.5=exp(-2*t/(RC)); ln(2) = 2*t/(RC), hence

    t= 2*5e5 *ln(2) /2 =346573.6s ≈ 4days;

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