The fundamental frequency component in the arm currents of a modular multilevel converter is a necessity for the operation of the converter, as is the connection and bypassing of the submodules. Inevitably, this will cause alternating components in the capacitor voltages. This paper investigates how the arm currents and capacitor voltages interact when the submodules are connected and bypassed in a sinusoidal manner. Equations that describe the circulating current that is caused by the variations in the total inserted voltage are derived. Resonant frequencies are identified and the resonant behaviour is verified by experimental results. It is also found that the effective values of the arm resistance and submodule capacitances can be extracted from the measurements by least square fitting of the analytical expressions to the measured values. Finally, the analytical expression for the arm currents is verified by experimental results.