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The figure shows a capacitor made of two circular plates,each of radius $12 \; cm$,separated by $5.0 \; cm$. The capacitor is being charged by an external source (not shown in the figure). The charging current is constant and equal to $0.15 \; A$.
$(a)$ Calculate the capacitance and the rate of change of potential difference between the plates.
$(b)$ Obtain the displacement current across the plates.
$(c)$ Is Kirchhoff's first rule (junction rule) valid at each plate of the capacitor? Explain.

The capacitance of a capacitor is $2 \ pF$. If the electric field inside the capacitor changes at a rate of $10^{12} \ V \ s^{-1}$,the displacement current is ..... $A$.

Match the following List-$I$ with List-$II$.
$A$. $\oint E \cdot dA$$(i)$ $0$
$B$. $\oint B \cdot dA$$(ii)$ $-\frac{d\phi_B}{dt}$
$C$. $\oint E \cdot dl$$(iii)$ $\frac{Q}{\varepsilon_0}$
$D$. $\oint B \cdot dl$$(iv)$ $\mu_0(i_c + i_d)$

$A$ parallel plate capacitor consists of two circular plates each of radius $2 \,cm$, separated by a distance of $0.1 \,mm$. If the potential difference across the plates is varying at the rate of $5 \times 10^6 \,Vs^{-1}$, then the value of displacement current is

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