AC-circuit with resistors and capacitors in series and parallel
Don't try to calculate any currents.  The circuit is set up as 2 voltage dividers. Calculate the voltage at A using the usual formulas for the impedance of a capacitor and a voltage divider.  Then calculate the voltage at B using the same formulas. Equate the two voltages (since if they are equal, there is no potential between A and B) and solve for the frequency. The answer is very simple in terms of R and C. Then substitute the given values of R and C to find the actual frequency.