Why does a filament lamp behaves in a way that does not follow ohm's law at higher voltage values?

Answer 1

Actually, everything follows Ohm's Law, you just have to consider dynamic resistance, i.e. the resistance at the precise operating point of the measurement.

A bulb has a positive temperature coefficient, or negative, depending on your point of view. My point of view is that, as temperature increases, the resistance increases, meaning a positive temperature coefficient. An alternate point of view, perhaps the common point of view, is that, as temperature increases, power decreases, meaning a negative temperature coefficient. Pick whichever point of view you want to use.

A typical 60 watt 120 volt bulb might have a 16 ohm cold resistance. (I just measured one.) If it kept that resistance, it would have an operating current by Ohm's law of 7.5 amperes, and a power of 900 watts. However, we know that it runs at 60 watts. Back calculating, that is a current of 0.5 amperes, and a resistance of 240 ohms hot. That a big difference from 16 ohms cold.

Now, that explains temperature coefficient. Lets look at compliance with Ohm's law, and the "theory" that some things do not comply...

Ohm's Law states that voltage is current time resistance. Period. It applies in every case. No exception. The problem is that you have to consider all of the parameters when you take that measurement, and the mistake people make is in assuming the resistance is constant. It is not. Not even for a simple resistor.

If you place two 60 watt bulbs in series across that same 120 volt supply, you will discover that they will run somewhat cooler, and that they have slightly less that 240 ohms resistance, but you can still calculate that resistance and you can still apply ohm's law. In this case, you will find that the power would be slightly more than 15 watts each, not the exactly 15 watts that you would expect based on constant resistance.

On a side note, reinforcing this concept, lets look at the forward bias characteristics of an ordinary silicon diode. This is a point of much contention, but I stand my ground on this...

As you increase the current through the diode, the voltage increases slightly. If it were a perfect diode, the voltage would not increase. If it were a resistor, it would track very close to Ohm's Law. Since it is a diode, it is somewhere in between. Does it obey Ohm's Law? Yes, it does. You simply pick a point, measure the conditions, and you can find the equivalent resistance of the diode at the point of current, and you will find that Ohm's Law will tell you what the voltage should be.

The same thing applies for AC circuits with inductive and capacitive reactance. Now we start talking about impedance and phase angle but, guess what, Ohm's law still applies - you just have to take everything into account.

Answer

In fact, not everything follows Ohm's Law. An incandescent lamp's filament (tungsten) is an example of a material that does not follow the law. This is because the current flowing through the filament is not proportional to the voltage applied to it. For a material to obey Ohm's Law, there mustbe a linear relationship between current and voltage.

In fact, Ohm's Law makes no mention of resistance. It merely states that 'the current flowing in a circuit is directly proportional to the applied voltage, provided external conditions, such as temperature, remains constant'. No mention of resistance; full stop.

The so-called 'Ohm's Law equation' only represents Ohm's Law when the resistance is a constant. Under all other conditions, the equation simply indicates what the resistance happens to be for specific values of voltage and current -it does not confirm Ohm's Law is being followed.