Question

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.

Answer 1

`C_(n et)=(C_1C_2)/(C_1+C_2)=2/3muF`
`q_(n et)=C_(n et)V`
`=(2/3muF)(1200V)`
`=800muC`
In series `q` remains same.
`:. q_1=q_2=800muC`
`V_1=q_1/C_1=800V`
and `V_2=q_2/C_2=400V`
b. Now, total charge will become `1600muC`. This will now distribute in direct ratio of capacity.
`:.q_1/q_2=C_1/C_2=1/2`
`q_1=(1/3)=(1600)=1600/3muC`
`q_2=(2/3)(1600)=((3200)/3)muC`
They will have a common potential (in parallel) given by
`V=("Total charge")/("Total capacity")`
`=(1600muC)/(3muF)`
`=1600/3V`