An inductor of inductance 2.0 mH is connected across a charged capacitor of capacitance $5.0 μ F$ and the resulting LC circuit is set oscillating at its natural frequency. Let $Q$ denote the instantaneous charge on the capacitor and $I$ the current in the circuit. The value of charge $Q$ is $100 μ C$ . Then the value of $| \frac{d I}{d t} |$ is $10^{x} A / s$ . Then $x$ value is

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Detailed Solution

$L = 2.0 m H = 2.0 \times 10^{- 3} H$
$C = 5.0 μ F = 5.0 \times 10^{- 6} F$
In an LC circuit, energy transfer continues from inductance to capacitance and vice versa.
By Kirchhoff’s law in an LC circuit
$\frac{Q}{C} + L \frac{d I}{d t} = 0 \Rightarrow \frac{d I}{d t} = - \frac{Q}{L C}$
$∴ | \frac{d I}{d t} | = \frac{Q}{L C} = \frac{100 \times 10^{- 6}}{2.0 \times 10^{- 3} \times 5.0 \times 10^{- 6}} = 10^{4} A s^{- 1}$