The resistance can not be calculated that way. If it was a low wattage resistor it is probably a fuse. There is no need of a resistor in bridge circuit. Even if you put a 1 ohm resistor it will burn out if it does not have sufficient wattage.

What comes from a bridge rectifier is 120V. broken DC, and that could quite possibly run a 120V. DC motor directly (with protection diodes to protect the bridge diodes). But you mention a capacitor, and presumably that is a filter cap. to smooth out the broken DC a bit.

The amount of smoothing is dependent on the current being drawn from the circuit, but if that is low, that capacitor tends to charge up towards (120 x 1.4142) = 169.7V.

MAYBE if the motor runs at a constant load, it may have had a series resistor to drop the excess voltage, so what is needed is the current drawn by the motor in operation.

But MAYBE also, the resistor was just a bleed resistor for the capacitor.

So, how does the circuitry connect, and what are the motor's ratings (voltage and current)?

I assume the RC filter is for brush noise. It would be an RC filter with 100uF cap and :

R= 1/2*π*√ RC= .159/(100E-6*60)= ~26.5?

You will need to know the current to compute the power.

incomplete information to answer your questin

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