1.

Capacitor C_3 in the circuit is a variable capacitor (its capacitance can be varied). C_1 and C_2 are of fixed values. Graph is plotted between potential difference V_1 (across capacitor C_1)versus C_3. Electric potential V_1 approches on asymptote of 10 V as C_3 prop oo. , Relation between C_1and C_2 is

Answer»

`C_1 = C_2`
`C_1 = 4C_2`
`4C_1 = C_2`
any relation

Solution :When `C_(3)toinfty` it means distance between the PLATES of `C_(3)` is zero or both plates will be at the same potential then `C_(2)` will be shorted entire pontential V will ber ACROSS `C_(1)` hence`V=V_(1)=10V`
Fromgraphs when `C_(3)=0,V_(1)=2V. So C_(3)` will act like open switch `C_(1)` and `C_(2)` will be in series potential different across `C_(2)` is `V_(2)=10-V_(1)`
`=8V`
`q=C_(1)V_(1)=C_(2)V_(2)` or `C_(12)=C_(28)` or `C_(1)=4C_(2)`
`V_(1)=4V,V_(2)=10-4=6V`
`q=C_(1)V_(1)=(C_(2)+C_(3))V_(2)`
or `C_(14)=(C_(2)+C_(3))6` or `16C_(2)=6C_(2)+6C_(3)`
or `C_(3)=5C_(2//3)`


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