| A conducting sphere S of radius 1 cm is connected to a parallel plate air capacitor C of plate area \[9\times {{10}^{-2}}\text{ }{{m}^{2}}\] and plate separation 8.85 mm. The capacitor is earthed with the help of switch S and inductor \[L=20\text{ }mH\] as shown in the figure. The sphere is imparted a charge \[{{q}_{0}}=36\,\mu C\] and switch is closed at t = 0. The maximum current in the circuit after closing the switch is |
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A) \[12\sqrt{10}A\]
B) \[24\sqrt{10}A\]
C) \[20\,A\]
D) \[10\,A\]
Correct Answer: C
Solution :
[c] Capacitance of sphere \[=4\pi {{\varepsilon }_{0}}R=90PF=C\] Capacitance of parallel plate capacitance \[=\frac{{{\varepsilon }_{0}}A}{d}=90PF=C\] At the instant of maximum current \[\frac{q_{0}^{2}}{2C}=\frac{{{\left( \frac{{{q}_{0}}}{2} \right)}^{2}}}{2C}\times 2+\frac{1}{2}LI_{\max }^{2}\] \[{{I}_{\max }}=20A\]
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