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Assuming your 10 ohm is not drifting you can probably calculate how much power is running through it by measuring the DC bus off the rectifiers with it as is and with the resistor shorted...That difference should give you the voltage drop across the resistor and P=(V^2)/R. You probably want a resistor rated at twice the power dissipation of the circuit so that it runs cooler...Many power resistors run almost hot enough to desolder themselves at their full rated power.
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