# How is power related to resistance ? (i.e. directly or inversely proportional) Please explain. Thank you !

Solution
As , P = V  I , where , P = Power , V = Voltage , I = current
So , by Ohm's law, voltage across a resistor is directly proportional to the current flowing through it,
i.e .,  V = I R
or I = V /R
So , P = V (V /R)
P = V2 / R
So , Power is inversely proportional to Resistance when voltage is constant.
Also P = I2R
So , Power is directly proportional to Resistance when current is constant.

There is no contradiction in the two equations since the current, potential, and resistance are related through Ohm's law (V=IR).
P = V2/R is used if the voltage is constant in which case the current also decreases when resistance increases. P= (I2)R should be used if the current is constant in which case the voltage also increases when the resistance increases

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