Question

The electric power consumed by a device may be calculated by using either of the two expression,P= VI or P= V^2R.
The first Expression indicates that it is directly proportional to R and in second expression ,it is showing that it is inversely proportional to the ​ R

How can the seemingly different dependence of P and R in these expression be explained?



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Answer 1

The expression for the power in the device can be calculated by using the formula :-

P = V I

We know that V = I R

Hence P = I²R

⇒ P ∝ R when I² is constant .

The second expression says :-

P = V²/R [ There is a mistake in typing ]

⇒ P ∝ 1/R where V² is a constant .

Hence there is no relation between both as the constants are different .

Infact if we put the value of V in the second equation we can get back the first equation .

P = ( IR )²/R

⇒ P = I²R

But Physics is logic , evidence , explanation and hence we need to explain the above fact .

If you notice carefully :-

P is inversely proportional to R when V² remains constant .

P is directly proportional to R when I² remains constant .

We know that P = W/t

P = I²Rt/t

⇒ P = I²R

Note that here P will change greatly if I² is increased or decreased and it will change more than R .

Δ P1 > Δ P2

When I² is constant , then R will change according to P and hence it is directly proportional.

When V² is constant :

P = I²R

Now if I² is increased , and V² is constant , then R will decrease automatically .

Now P will increase because it is dependent on I more than R .

If I² is decreased , V² remains constant but R decreases .

P will increase as it is dependent on I² and Δ P1 > Δ P2 .

This explains the expression . Power will change more if current is changed than if resistance is changed .

Answer 2

Answer:

A) Both the expressions are correct. In the first case, I remain constant whereas the second expression is true when V remains constant

So, the expression P = I2R is used when resistances are connected in series because in series connection the current in each resistance is constant.

Similarly, when resistances are connected in parallel the voltage is constant and so power becomes inversely proportional to R.

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