I know the answer is D, but I cannot figure out why? 7. An EMF source with a vol

Question

I know the answer is D, but I cannot figure out why?

7. An EMF source with a voltage V, a resistor with a resistance R and a capacitor with a capacitance C are connected in series. Initially a switch in this circuit is open. At time t = 0 the switch is closed and the capacitor starts to charge. Which of the following statements about the current I in the circuit and the charge Q on the capacitor is TRUE? a) When I = 0, Q = 0. b) When I = V/4R, Q = CV/4. c) When I = V/R, Q = CV. d) When I = V/4R, Q = 3CV/4. e) When I = V/2R, Q = 2VC.

Explanation / Answer

apply   charge Q = Qmax (1-e^-t/RC)

and I = Io ( e^-t./RC)

apply these two wauation at each set of the given options and verfiy

so at option D :

asV/R = Io

I = Io/4

so e^-t/RC = 1/4 = 0.25

-t/RC = ln (0.25) = -1.386

t = 1.386 * RC

---------------------

so at this time cosnatnt, what happens at charge is ?

Q = Qmax( 1- e^-1.386)

Q = 0.75 Qmax   = 0.75 CV   = 3CV/4

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