  Whether astrophysical black holes (BHs) can have charge is a question to be
addressed by observations. In the era of gravitational wave (GW) astronomy, one
can constrain the charge of a merged BH remnant using the merger-ringdown
signal of the GW data. Extending earlier studies, we analyze five GW events in
GWTC-3, assuming Kerr-Newman BHs. Our results show no strong evidence for a
charged BH, and give a limit on the charge-to-mass-ratio $Q<0.37$ at $90\%$
credible level (CL). Due to the charge-spin degeneracy in the waveform and the
limited signal-to-noise ratios (SNRs), it is challenging for LIGO/Virgo/KAGRA
observations to provide better constraints. We further simulate data for the
Einstein Telescope (ET), where SNRs can be as large as $\sim270$ in the
ringdown signal. These simulated events allow us to consider the 220, 221, and
330 ringdown modes altogether, which can help break the charge-spin degeneracy.
The analysis of a simulated GW150914-like signal shows that ET can improve the
constraints on the charge-to-mass-ratio to $Q \lesssim 0.2$ at $90\%$ CL with
one ringdown signal.
