A `1muF` capacitor and a `2µF` capacitor are connected in series across a `1200 V` supply line.
a. Find the charge on each capacitor and the voltage across them.
b. The charged capacitors are disconnected from the line and from each other and reconnected with terminals of like sign together. Find the final charge on each and the voltage across them.

Options

A. Charge on capacitors are `1400//3 muF` and `3200//3 muF` and potential deffernce across each capacitor is `1600//3 V`.
B. Charge on capacitors are `1600 muC` and `3200//3 muC` and potential differnce across each capacitor is `1600//3` V`.
C. Charge on each capacitor is `1600 muF`, and potential difference across each capacitor is `800 V`.
D. Charge and potential difference each capacitor are zero.

Answer

D

Explanation

.
`1200-q/1-q/2=0` or `q=800 mu C`
Charge on each capacitor is `800 muC`.
`V_(1)=q/C_(1)=(800)/1 =800 V`
`V_(2)=q/C_(2)=(800)/2=400 V`
.
(i) `q'_(1)+q'_(2)=1600`
Also, `(q'_(1))/1-(q'_(2))/2-0`
or `q'_(2)=2q'_(1)`
From Eq. (i), `3q'_(1)=1600` or `q'_(1)=(1600)/3 mu C`
`3q'_(2) =(3200)/3 muC`
`V=(q_(1)+q_(2))/(C_(1)+C_(2))=(1600)/3 V`
(ii) `q'_(1)+q'_(2) =800-800=0`
Also, `(q'_(1))/1-(q'_(2))/2=0`
.
From Eq. (ii), `q'_(1)=q'_(2)=0`
Therfore, potential differnce across each capacitor zero.