Resistivity is the property of material, and it is almost constant, while capacitance of the material is the property. which varies with saturation, depends on variation of charge with the variation of voltage which is not remaining constant, hence you cannot apply the Ohm's law.

Dear Bhupendra Desai

Ohm's law states that voltage is equal to current times resistance. This is always true. DC, AC, RF, whatever. Resistance, capacitance, or inductance, whatever. Its a matter of proper perspective, and its a matter of taking everything into account. Some devices do not have a linear response to voltage or current. Take the light bulb, for instance. If you measures its resistance you can calculate what you think its current and power would be at a certain voltage, and you would be wrong, unless you also considered temperature. This is because light bulbs have a very dynamic resistance to temperature coefficient. For another example, look at the diode. Initially, it appears to have high resistance. When the voltage across it reaches the forward bias voltage (or the reverse bias voltage for a zener diode) it starts to conduct and draw current. As you increase the current, you note that the voltage is relatively constant. That is certainly not a resistor - the diode's resistance is increasing as current increases so as to make the voltage be somewhat constant. You can still calculate voltage, current, resistance, and power, but only at each point of observation. consider the capacitor. In a DC circuit, the capacitor initially has zero ohms resistance, but it quickly rises to infinity ohms depending on current and capacitance. In an AC circuit, this a much more interesting and useful case the capacitor stabilizes at a certain capacitive reactance, and the operation of the circuit complies with Ohm's law. you find that the current is no longer in phase with the voltage. While this complicates calculations, nothing changes the fact that voltage is current times resistance. That is an immutable given - your task is to learn how to measure it correctly.in each of these cases, and in any other case, Ohm's law applies, but it applies in a certain way, under a certain set of circumstances.

Ohm's 'Law' is somewhat of a misnomer, because it is not really a universal law because it only applies to a small range of conductors. Ohm's Law only applies when the ratio of voltage to current is constant for variations in voltage. Devices that follow Ohm's Law are called linear or ohmic; those that don't are called non-linear or non-Ohmic. Most metal conductors are linear, but some are not. For example, tungsten does not obey Ohm's Law because its ratio of voltage to current changes as the voltage applied across it changes -in other words, tungsten is non-linear devices, Electronics devices such as diodes, electrolytes, and gases are all non-linear and do not obey Ohm's Law. Having said that, the ratio of voltage to current will always tell you what the resistance of a device devices, such as diodes, electrolytes, and gases are all non-linear and do not obey Ohm's Law. Having said that, the ratio of voltage to current will always tell you what the resistance of a device happens to be for that particular ratio and, so, the equation R = V/I applies to all devices whether they are linear or non-linear. However, this equation is not derived from Ohm's Law, but from the definition of resistance.

Dissipation current in a capacitor exists when applied source is AC. because electric field is variable in this case. While in case of DC source dissipation current exists only for a very small time ( says fraction of second) until the capacitor is fully charged. In case of ac source it has a fixed frequency and at this fixed frequency reactance (1/jWc) of capacitor is also fixed. so undoubtedly we can apply Ohm's law. If we do frequency domain analysis then we can observe that output across a capacitor has same frequency component as input i.e. it doesn't produces harmonics hence capacitor is a linear circuit element like resistor and we can apply Ohm's law.

Dear Nandan Kumar Jha and Bhupendra Desai, As you are younger to me hence boldly I can say "Do not argue beyond the boundary of the fact of Ohm's law":

Look materials obeying are obeying the Ohm's Law. We can call those materials as 'Ohmic' materials. Some materials do not satisfy this Law like simple light bulbs, LED, ...

Capacitance is materialistic property which opposes the rate of change of voltage. And I appreciate Bhupependra Desai's approach. As Nandan Kumar is writing about reactance is good approach but not that much strong as Desai has hammered at right spot. Here the question is we designed capacitor to that. When you apply Ohm's Law you have to plot I vs dVc/dt and that is Obeying Ohm's law.

Dr. Afaq Ahmad

Here i think i didn't go beyond the boundary of Ohm's law. There is a bit modification in Ohm's law where voltage is still resistance(here it is reactance ) times of current but the modification is here current and voltage are not in phase...unlike original forms of Ohm's law (V=R.I)

Displacement current (i=C dv/dt) is the formula you cite. It isn't really related to Ohms law, it is just in a similar form. In order to derive the formula you actually use electromagnetic theory and Maxwell's equations. Conduction current is zero for an IDEAL capacitor, which is what we deal with in most circuit theory classes. For a real world capacitor, there is always a (very large but not infinite) resistance across the dielectric material between the two capacitive plates. This is why a charged capacitor (i.e. hook the leads up to a battery then remove the battery) eventually discharges. It is as if there is an extremely large resistor in parallel with the ideal capacitor. That resistor follows ohm's law. The 'better', i.e. more expensive the capacitor, the higher the internal resistance, and the smaller that conduction current is. Hope that helps.

Ohm’s law refers to conductive media only, with finite values for the resistivity (ro) or conductivity (sigma), where sigma=1/ro. Its local form states that the current density (J) is equal to the product between the conductivity (sigma) and the electric field strength (E) in any point of the conductive media. In this case, the term “current” refers to conduction current, also the flow (with finite macroscopic speed) of electrons through solid conductive media or of ions in electrolytes.

Regarding the dissipation (displacement) current, it is linked to the time-variant magnetic filed in dielectric media or in free space (it is equal to the derivative with respect to time of the magnetic flux through a given surface). Please see again the Ampere’s circuital law in the form given by Maxwell !

The expression i=C*dV/dt for capacitors is something different: it is a consequence of the law of conservation of electric charge expressed for a closed surface surrounding one of the capacitor plates.

Dear Nandan Kumar Jha,

Materials are obeying the Ohm's Law. We can call those materials as 'Ohmic' materials. Some materials do not satisfy this Law like simple light bulbs, LED, ...

Capacitance is materialistic property which opposes the rate of change of voltage. And this property we got in our circuit theory like i = C (dVc/dt) which came from the Ohm's law.

Let me asure you Nandan, that the displacement current is 100% real. Actually you can measure it if you put a current clamp in the empty space between the capacitors plates. The problem lies with the definition of current: of course there are no charged particles flying accross the plates of the capacitor! But there is an energy exchange taking place, which can be attributed to a current. It is the same current you would measure with an Ammeter in series with the conductor suplying the voltage to the capacitor.

In the frequency domain a capacitive reactance=1/(Cω) causes a voltage drop of I/(Cω) accross the capacitor. So, if you consider 1/(Cω) as the resistance of the capacitor then Ohm's law applies 100%. In the time domain you can not do this so easily. You can assign a dynamic resistance to the capacitor, which changes with time, but it will give you no actual insight into the behaviour of the capacitor:

http://www.informit.com/articles/article.aspx?p=102225&seqNum=5

Dear Dimitrios

Thanks for your valuable opinion

Now, I got the theory and ideals behind this topic. So if we are going to apply Ohm's law to a capacitor, then we have to analysed it into frequency domain. In time domain it is very complicated to solve the issue. And it is also clear that if we apply a voltage across a capacitor, which has harmonics ( unlike sinusoidal waveform) then its impedance in frequency domain will not constant with frequency and Ohm's law is not applicable.