$A$ parallel plate capacitor has a capacitance $C = 200 \ pF$. It is connected to a $230 \ V$ $AC$ supply with an angular frequency $\omega = 300 \ rad/s$. The $rms$ value of the conduction current in the circuit and the displacement current in the capacitor,respectively,are:

  • A
    $1.38 \ \mu A$ and $1.38 \ \mu A$
  • B
    $14.3 \ \mu A$ and $143 \ \mu A$
  • C
    $13.8 \ \mu A$ and $138 \ \mu A$
  • D
    $13.8 \ \mu A$ and $13.8 \ \mu A$

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Match the following List-$I$ with the List-$II$:
List-$I$List-$II$
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$(B)$ Faraday's law$(II)$ Electric charge and energy conservation
$(C)$ Ampere's law$(III)$ Change in magnetic flux
$(D)$ Kirchhoff's law$(IV)$ Change in electric flux
$(V)$ Total electric flux

Consider three quantities $x = E/B$,$y = \sqrt{1/(\mu_0 \varepsilon_0)}$ and $z = l/RC$. Here,$l$ is the length of a wire,$C$ is capacitance,and $R$ is resistance. All other symbols have standard meanings. Which of the following statements is correct?

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$A$ physical quantity $\vec{S}$ is defined as $\vec{S}=(\vec{E} \times \vec{B}) / \mu_0$,where $\vec{E}$ is the electric field,$\vec{B}$ is the magnetic field,and $\mu_0$ is the permeability of free space. The dimensions of $\vec{S}$ are the same as the dimensions of which of the following quantity(ies)?
$(A)$ $\frac{\text{Energy}}{\text{charge} \times \text{current}}$
$(B)$ $\frac{\text{Force}}{\text{Length} \times \text{Time}}$
$(C)$ $\frac{\text{Energy}}{\text{Volume}}$
$(D)$ $\frac{\text{Power}}{\text{Area}}$

For an $EM$ wave,the electric and magnetic fields are $300 \ V m^{-1}$ and $7.9 \ A m^{-1}$ respectively. The maximum rate of energy flow is, (in $W m^{-2}$)

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