Given a set of resistors connected in series to an AC power supply: What formula

Question

Given a set of resistors connected in series to an AC power supply:

What formula governs the peak-to-peak voltage which will be measured when voltage is probed over individual resistors and sets of resistors in that circuit?
What is a good way to think about this construction so the answer to question #1 is obvious and intuitive?

Intuitively, I would think that the measured voltages would be the same as in a DC circuit such that:

V_out = (R_partial/R_total) V_in

Where V_out is the voltage which is probed, R_partial is the total resistance of the sub-set of resistors which are being probed and R_total is the total resistance in the circuit.

This formula makes sense intuitively because the current throughout a circuit of series components is everywhere constant and according to Ohm's law for a constant current, the higher a given resistance over an area the higher the voltage potential measured there.

Is this correct for AC circuits as well?

Explanation / Answer

Your equation/setup is essentially correct as long as we are talking about idealised resistors, ie they have no complex impedance.

To deal with time varying currents and/or voltages we generalise the concept of resistance to impedance. Impedance takes into account any delay/lag between resistive components and the voltage across them. In an idealised resistor this lag is zero and hence the impedance = the resistance and so your setup holds. A circuit containg capacitance/inductance will display more complex behaviour however.

For further guidance I suggest investigating 'impedance'

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