According to Ohm’s Law, I ∝ V, But I ∝ 1/V in Power Equation. Explain?

Electrical Technology

In I = V ÷ R, Current is Directly Proportional to the Voltage, But Current is Inversely Proportional to the Voltage in P = V × I?

This is another confusing question mostly asked in electrical and electronics engineering interviews as is follow.

According to Ohm’s Law, Current Increases when Voltage increases (I=V ÷ R), but Current decreases when Voltage increases according to (P = V × I) formula. How do you explain?

i.e.

According to Ohm’s Law: I ∝ V (Current directly proportional to the Voltage. I = V ÷ R)
According to Power Formula: I ∝ 1 ÷ V (Current is inversely proportional to the Voltage. I = P ÷ V)

In short, according to the Ohm’s Law (V = I × R or I = V ÷ R) which shows that Current is directly proportional to the Voltage, but according to P = V × I or I = P ÷ V, it shows that Current is inversely proportional to the Voltage.

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Let’s clear the confusion about the statement.

P = V × I

Actually, it depends on how you increase the parameters i.e. if you increase the voltage by keeping the power of the source constant or is it varying.

If the power of the source is constant then the current would decrease when voltage increases.
If you don’t care about the power and just simply replace the battery with a new one’s with higher power rating this can increase the current when voltage increase as power is no more constant i.e. power has been also increased.

In case of transformer, when voltage increases then current decrease because power remains constant i.e. both side power is P = VI (neglecting the power factor: Cos θ).

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V = I × R

By Ohm’s Law, Current (I) is directly proportional to the Voltage (V) if Resistance (R) and Temperature remain constant.

V = I × R
R = V ÷ I
I = V ÷ R

According the power formula, It says that Current is inversely proportional to the voltage if power remain same.

P = V × I
I = P ÷ V
V = P ÷ I

As we already know that in a step-up transformer, if voltage increases, the current decreases where power is same (as transformer only step-up or step-down the value of current and voltage and doesn’t change the value of power). Similarly, voltage decreases when current increases in a step-down transformer.

The same story is there at the generating station where power generation is constant. If power at generation side improves, both current and voltage will be increased.

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In short:

If power is constant = Voltage is Inversely proportional to the Current i.e. V ∝ 1 ÷ I in P = V × I.
If resistance and Temperature are constant: Voltage is directly proportional to the Current i.e. V ∝ I in V = I × R.

That’s is the exact reason why in Ohm’s Law, Current is Directly Proportional to the Voltage But Inversely Proportional to the Voltage in Power formula.