In the circuit in fig. If no current flows through the galvanometer when the key k is closed, the bridge is balanced. The balancing condition for bridge is

Options

A. `(R_(1))/(R_(2))=(C_(1))/(C_(2))`
B. `(R_(1))/(R_(2))=(C_(2))/(C_(1))`
C. `(R_(1))/(R_(1)+R_(2))=(C_(1))/(C_(1)-C_(2))`
D. `(R_(1))/(R_(1)-R_(2))=(C_(1))/(C_(1)+C_(2))`

Answer

C

Explanation

At balance the potentials of point B and D are same ad there will be no current in the arm BD. Thus,
where q is the charge on both the capacitor plates connected is series
Quite similarly `V_(B)-V_(C)=V_(D)-V_(C)`
or `i_(1)R_(2)=(q)/(C_(2))` ..(ii)
dividing eqs (i) and (ii), we get
`(R_(1))/(R_(2))=(C_(2))/(C_(1))`