InterviewSolution
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InterviewSolution
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An isolated parallel plate capacitor has circular plates of radius `4.0cm`. If the gap is filled with a partially conducting material of dielectric constant `K` and conductivity `5.0xx10^-14Omega^-1m^-1`. When the capacitor is charged to a surface charge density of `15muC//cm^2`, the initial current between the plates is `1.0muA`? a. Determine the value of dielectric constant `K`. b. If the total joule heating produced is `7500J`, determine the separation of the capacitor plates. |
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Answer» a. This is basically a problem of discharging of a capacitor from inside the capacitor. Charge at any time `t` is Here, `q_0=` (area of plates )(surface charge density) and discharging current, `i=((-dq)/(dt))=q_0/tau_C.e^(-t//tau_C)=i_0e^(-t//tau_C)` Here `i_0=q_0/tau_C=q_0/(CR)` `C=(Kepsilon_0A)/d` and `R=d/(sigmaA)` `:. CR=(Kepsilon_0)/sigma` Therfore, `i_0=q_0/((Kepsilon_0)/sigma)=(sigmaq_0)/(Kepsilon_0)impliesK.(sigmaq_0)/(i_0epsilon_0)` substituting the values, we have `K=((5.0xx10^-14)(pi)(4.0)^2(15xx10^-6))/((1.0xx10^-6)(8.86xx10^-12))=4.25` b. `U=1/2q_0^2/C=1/2q_0^2/((Kepsilon_0A)/d)` `:. d=(2Kepsilon_0AU)/q_0^2` `=(2xx4.25xx8.86xx10^-12xxpixx(4.0xx10^-2)^2xx7500)/((15xx10^-6xxpixx4.0xx4.0)^2)` `=5.0xx10^-3m=5.0mm` |
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