see answers to this question.
Is a capacitor really necessary? And wouldn't it make measurements frequency-dependent?
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A series capacitor acts as an high-pass filter, also known as AC-coupling capacitor. The reason is that for DC current, a capacitor is like an open circuit, whereas for higher frequencies (depending on C and the other resistances) it becomes more like a short circuit, if it's big enough.
The measurements will be indeed frequency dependent, but if the frequency is high enough the signal will fall in the right part of the curve, which is approximately flat.
So it's an useful tool, but to be used carefully. The same happens with scopes, where leaving the AC coupling on when measuring signals will distort them, like this square wave:
A series capacitor is not necessary to measure AC.
A capacitor to ground may be used to filter the derived DC.
Some meters do not utilise series capacitors.
The meter in the previous question MAY use a capacitor somewhere in the circuit but it is at least partially DC coupled as it reads 2VAC for every 1VDC when DC is applied. I have seen this behaviour frequently in the past with analog meters. The meter in the previous question may be an analog meter.
Use of a series capacitor allows DC components to be easily eliminated. This may or may not be desirable depending on the circuit used.
A series capacitor will cause some low frequency roll off but as the circuit can easily be very high impedance overall a modest value of capacitance will allow almost 'flat'measurement at mains frequencies. "AC" is usuallty 50 or 60 Hz in the large majority of cases.
If one will allow of the use of the dread Gargoyle in an answer then this link will be most informative regarding typical practice
Below is the circuit of an entry level "yellow' multimeter as found in zillions all over. Circuit diagram quality is only about 0.27 Olins but sufficeth for this task. It appears to use a simple half wave rectifier with no series capacitor. C_unreadable at left centre to the right od D_unreadable aoppears to be smoothing of sorts. [Far better circuit both in circuitry and in Olins is here and many more via gargoyle image link above.
Note: Use of Gargoyle image link here seems a very very good and appropriate use of the facility in an answer. If any disagree please advise and my second will call. [ :-) ].
If the AC signals you want to measure are pure AC, without DC component, it would be better not to have the series capacitor. You would only get a wrong reading when measuring DC.
If your AC signal is superposed to DC the capacitor will block the latter and only let the AC pass. The circuit which converts the AC to it's average will give a wrong reading if there's a DC component present.
And yes, the result is frequency dependent. A DMM will be tuned to measuring mains frequencies, i.e. 50Hz or 60Hz.
In fact, and now that you ask, a "true-RMS" volt/ampmeter should not have a capacitor in series, because the true RMS of a DC input is that DC value itself, and a series capacitor would just make that reading impossible.
Anyway, to answer your question, yes, a capacitor makes the measurement frequency dependent.
DC can't cross the capacitor - only the AC components of a signal can. If you want to measure only AC then some method to block the DC component of a signal is necessary.
It will cause some frequency dependence, but the manufacturer can match the capacitor size to the internal resistance of the measurement device and choose the frequency response of the circuit to accommodate most signals.