A 290-Ω resistor is connected in series with a 4.10-μF capacitor and a source of time-varying emf providing 70

A 290-Ω resistor is connected in series with a 4.10-μF capacitor and a source of time-varying emf providing 70.0 V.

a) At what frequency will the potential drop across the capacitor equal that across the resistor?

You need to define exactly what this "time-varying emf" means.

Your use of the word "frequency" implies that this is a sine wave that can be varied in frequency, but that is just a guess, there could be many other possibilities.

Assuming the above, that means the capacitive reactance equals 290 ohms

Capacitive Reactance Xc = 1/(2πfC)
1/(2πfC) = 290
f = 1 / [ 2π(290)(4.1e-6) ]
f = 133.9 Hz