Power is inversely proportional to resistance.
Ohm's law: Current is voltage divided by resistance
Power law: Power is voltage times current, therefore power is voltage squared divided by resistance.
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Power can be measured in Watts = Amps x Volts x Power Factor. Volts = Current x Resistance. For a resistive load PF = 1. Therefore, Power = Current squared x Resistance.
All resistances will emit heat energy when a current flows. The heat production rate (or power) can be found by any of these formulas: Power = Current * Voltage Power = Current2 * Resistance Power = Voltage2 / Resistance. Power is given in Watts when Current is in Amps, Voltage in Volts, and Resistance in Ohms.
The power dissipated across a resistor, or any device for that matter, is watts, or voltage times current. If you don't know one of voltage or current, you can calculate it from Ohm's law: voltage equals resistance times current. So; if you know voltage and current, power is voltage times current; if you know voltage and resistance, watts is voltage squared divided by resistance; and if you know current and resistance, watts is current squared times resistance.
When voltage and current waveforms are out of synch the power factor is reduced. In a pure resistance load the PF is 1. When inductance and capacitance is involved the PF is from 0 to 1.
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First, this statement stands as long as voltage is constant. If you held the current constant then power would increase as resistance increases.V=IR. For a fixed voltage if you increase the resistance (R) then the current (I) will decrease - following the formula.Power = VI so as the resistance increases the value of VI (power) decreases as V is constant and I gets smaller.Therefore the power is decreasing as the resistance increases (when voltage is held constant).Hope this helps.