Question 11 Mark
shows a capacitor made of two circular plates each of radius $12 \ cm,$ and 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 $ 0.15A.$
- Calculate the capacitance and the rate of charge of potential difference between the plates.
- Obtain the displacement current across the plates.
- Is Kirchhoff’s first rule $($junction rule$)$ valid at each plate of the capacitor? Explain.
Answer
View full question & answer→Radius of each circular plate $, r = 12 \ cm = 0.12 m$ Distance between the plates $, d = 5 \ cm = 0.05 m$ Charging current $, I = 0.15$ A Permittivity of free space $,\varepsilon_0=8.85\times10^{-12} \ \text{cm}=0.12 \ \text{m}$
$=\frac{8.85\times10^{-12}\times\pi\times12^2}{0.05}$
$V =$ Potential difference across the plates
Differentiation on both sides with respect to time $(t)$ gives:
But $, \frac{\text{dq}}{\text{dt}}=\text{current }(I)$
Therefore, the change in potential difference between the plates is $1.87\times10^9\text{V}/\text{s}$.
- Capacitance between the two plates is given by the relation,
$=\frac{8.85\times10^{-12}\times\pi\times12^2}{0.05}$
$V =$ Potential difference across the plates
Differentiation on both sides with respect to time $(t)$ gives:
But $, \frac{\text{dq}}{\text{dt}}=\text{current }(I)$
Therefore, the change in potential difference between the plates is $1.87\times10^9\text{V}/\text{s}$.
- The displacement current across the plates is the same as the conduction current. Hence, the displacement current $, i_d$ is $0.15 A.$
- Yes