In the circuit shown in figure, if the charge on capacitor `C_(2)` in steady state is `(10x)/3 muC`, then find value of `x`.
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Answer

3

Explanation

During the steady state the capacitors are fully charged and will behave like open circuit. So the current will flow outer loop only. The current in the outer loop will be `=30/10=3` Amp. in clockwise direction. Charge distribution on the plates of capacitors are as shown in figure.
Applying KVL in loop -I
`q/2+(q_(1))/2-15=0impliesq+q_(1)=30`.........(1)
Applying KVL in loop -II
`(q-q_(1))/10-6+10-(q_(1))/2=0`............(2)
On solving equation (1) and (2) we get `q_(1)=10mu C`