Please show full step by step solution for full rating A capacitor C and resisto

Question

Please show full step by step solution for full rating

A capacitor C and resistor R are connected in series and used as a timing circuit. First the capacitor is charged (by some external power source) so that there is a potential difference V0 between its plates. Then a switch completing the timing circuit is closed and the capacitor begings to discharge as current flows through the resistor. What is the charge on the capacitor as a function of time? At what time is the charge on the capacitor 37% its initial value? at t = RC at f = l/RC at t = e-1 at t = e Explain your reasoning referring to the equation you found in (a). What is the current through the resistor as a function of time? What is the power used by the resistor as a function of time?

Explanation / Answer

a) Q=Q0*exp(-t/RC)

Q0=V0*C

b) at t=RC

Exp(-t/RC)=exp(-1)=0.37

==> Q=Q0*0.37

i.e 37 % of initial chanrge

c) i=dQ/dt=-(Q0/RC)*exp(-t/RC)

where Q0=V0*C

d) power =i^2R=(Q0/RC)^2*exp(-2t/RC)*R=V0^2/R*exp(-2t/RC)

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