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According to P=IV, if P is constant with increase in I (current,) then voltage has to decrease and vice a versa - which means they become inversely proportional but according to Ohm's law they are directly proportional. What role does resistance play?

According to Ohm's law V~I. But R should also be directly proportional to current as with increase in current heat increases and with heat increase resistance increase. As H=I^2RT therefore, with increase in current the resistance increases but due to resistance increase current will decrease and therefore resistance shall also decrease.

Please clear the confusion between relation of formulas.

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  • \$\begingroup\$ Ohm's law doesn't apply to everything; only to resistive loads. For example, diodes, transistors, transformers, motors, capacitors, and inductors are not governed by Ohm's law. Only resistors follow V=iR. \$\endgroup\$ – MarkU Dec 23 '19 at 9:38
  • \$\begingroup\$ R, L & C are passive circuit constants. Their value depends upon physical properties such as length, cross-sectional area of element and material they're made up of. If you apply constant V across constant R, I that will flow through R is fixed. Now, if you increase V, I will increase. R varies with temperature yes, then I at any instant will depend upon value of R at that instant. If R keeps changing, I will keep changing, Ohm's law would still be valid at every instant. \$\endgroup\$ – Deep Dec 23 '19 at 12:14
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Answering about Ohms law:

Ohm's law has sometimes been stated as, "for a conductor in a given state, the electromotive force is proportional to the current produced." That is, that the resistance, the ratio of the applied electromotive force (or voltage) to the current, "does not vary with the current strength ." The qualifier "in a given state" is usually interpreted as meaning "at a constant temperature"

from: https://en.wikipedia.org/wiki/Ohm%27s_law#Temperature_effects

You are right about the change in resistivity due to change in the temperature. The resistivity has a dependency on temperature. Ohm's law hence is primary defined in a given state. At a constant applied voltage, the current would decrease as in case of conductors and the current would increase as in case of semiconductors. Ohm's law is applicable in a given state. hence, the variable temperature will not be considered.

https://www.askiitians.com/iit-jee-electric-current/temperature-dependence-of-resistivity/

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According to P=IV ,IF P is constant With increase in I (current) Voltage has to decrese and vise a versa ..Which means they become inversely proportional but according to ohm's law they are directly proportional .What role does resistance play

$$ P=VI$$ $$V=IR$$ Combing gives $$ P=V^2/R$$ or $$ P=I^2R$$

If P is constant, and V changes or I changes, then, R has to change.

If R cannot change, then, the assumption P is constant is false.

According to OHM'S law .. V~I. But R should also be directly proportional to current as with increase in current Heat Increases and with Heat increase resistance increase. As H=I^2RT There fore , with increase in current the resistance increases but due to resistance increase current will decrease and therefore resistance shall also decrease Please clear the confusion between relation of formulas ..

This bold marked text is incorrect. You assumed P to be constant. So, heat will not increase with current, it will only increase with time. $$ H=PT=I^2RT $$

where capitcal T is time.

According to OHM'S law .. V~I. But R should also be directly proportional to current as with increase in current Heat Increases and with Heat increase resistance increase. As H=I^2RT There fore , with increase in current the resistance increases but due to resistance increase current will decrease and therefore resistance shall also decrease Please clear the confusion between relation of formulas ..

If resistance changes, the the assumption P is constant is false.

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Let's put our thoughts in order ...

Ohm's law is about linear (constant) resistance. This means we must not allow warming. In this arrangement we begin to experiment.

First, we connect a voltage source to the resistor and begin varying the voltage across it. As a result, the current through the resistor will proportionally vary - Iout = Vin/R. If we vary the resistance, the current will inverse proportionally vary - Iout = V/Rin.

Then, we connect a current source to the resistor and begin varying the current through it. Now the voltage across the resistor will proportionally vary - Vout = Iin.R. If we vary the resistance, the' voltage will proportionally vary - Vout = I.Rin.

In all these experiments, the power will vary since Pout = Vin^2/R or Pout = Iin^2.R. If you want to keep it constant, change the resistance in the respective direction. This means there are two input variables in Ohm's law - Iout = Vin/Rin and Vout = Iin.Rin, or the resistance has become "dynamic".

Such tricks are used to make non-linear resistors that keep constant voltage (e.g., a Zener diode) or constant current (e.g., a transistor). It can be seen from the IV diode curve and transistor output characteristic.

Of course, we can keep constant power according to Pout = Vin.Iin. This means to connect a voltage source to current source. Thus the voltage source will set the voltage across sources and the current source will set the current through them. More precisely speaking, in this arrangement only one of the elements is a source; the other is a load implemented as a non-linear resistor.

Now, to keep constant power, when increasing the voltage, we decrease the current and v.v. But actually we can do it only by changing the resistance (there is no other way to change the current or voltage). That is why the arrangements above are more suitable for the purposes of intuitive understanding.

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