The simplest formula for conduction current,displacement current and loss tangent

[veinn]

Apparently my lecturer has given me this type of quest and i really have no idea how to do this quest..anyone know the formula for conduction current..displacement current and loss tangent..please give me brief idea how to do it...what i know is that for displacement current i have to differentiation..but how??pleasezz help meeee

A parallel plate capacitor consists of two metal plates, of area 2 cm2, separated by 3 µm of porcelain with єr =5.7 and =2 X 10-13 Sm-1. The capacitor is connected to a 12 volt 50 Hz supply. Determine the conduction current, and compare it to the displacement current. In addition, calculate the loss tangent at frequencies of 50 Hz, 1 MHz, and 100 MHz

 

[marlon]

The conduction current is $$I =C * \frac {dV}{dt}$$

You know how V varies with respect to t. You will need to find C, which is not that difficult.

The displacement current D can be calculated from

$$\frac{\partial D}{\partial t} = - \frac{\epsilon}{w} * \frac{dV}{dt}$$
w is the distance between the condensatorplates. Keep in mind that there is porcelain between the plates.

I am not too sure what you mean by loss tangent, but i think this is a language problem :) ?

marlon

ps : this is just a general overview to get you started on this one. I am not allowed to give too much info for the obvious reason

 

[thepatientmental]

The simplest formula for conduction current is I = V/R, where I is the current, V is the voltage, and R is the resistance. In this case, the resistance will be the resistance of the porcelain material, which can be calculated using the formula R = ρl/A, where ρ is the resistivity of the material, l is the distance between the plates, and A is the area of the plates.

To calculate the displacement current, we use the formula I = ε0εr(dV/dt), where I is the displacement current, ε0 is the permittivity of free space, εr is the relative permittivity of the material between the plates, and dV/dt is the rate of change of voltage with respect to time. In this case, we can find the value of dV/dt by dividing the given frequency (50 Hz) by the voltage (12 V).

For the loss tangent, we use the formula tanδ = εrIm(σ)/ε0Re(σ), where tanδ is the loss tangent, εr is the relative permittivity, Im(σ) is the imaginary part of the conductivity, and Re(σ) is the real part of the conductivity. In this case, we can find the values of Im(σ) and Re(σ) using the given frequency and conductivity.

To solve the given problem, we first need to calculate the resistance of the porcelain material. Using the given values, we can find the resistivity (ρ) using the formula ρ = 1/σ, where σ is the conductivity. Plugging in the given conductivity, we get ρ = 5 X 10^12 Ωm. Using this value and the given distance between the plates (3 µm), we can calculate the resistance using the formula R = ρl/A. This gives us a value of 75 X 10^6 Ω.

Next, we can find the displacement current using the formula I = ε0εr(dV/dt). Plugging in the given values for ε0, εr, and dV/dt, we get a displacement current of 3.4 X 10^-12 A.

To find the loss tangent, we need to calculate the values of Im(σ) and Re(σ) at each given frequency. Using the given conductivity and frequency, we can calculate the values of Im(σ