Question

A RC series circuit of $ R = 15\Omega $ and $ c = 10\mu F $ is connected to $ 20volt $ DC supply for a very long time. Then the capacitor is disconnected from the circuit and connected to the inductor $ 10mH $ . Find the amplitude of the current.
 $ \left( A \right){\text{ 0}}{\text{.2}}\sqrt {10} A $
 $ \left( B \right){\text{ 2}}\sqrt {10} A $
 $ \left( C \right){\text{ 0}}{\text{.2A}} $
 $ \left( D \right){\text{ }}\sqrt {10} A $

Answer 1

Hint: To solve this we need the formula of the amplitude of the current and is given by $ {I_ \circ } = {Q_ \circ }w $ and we also know that the charge is given by, $ {Q_ \circ } = C{V_ \circ } $ , so by using all these formulae we will be able to solve this question.

Formula used:
The amplitude of the current is given by,
 $ {I_ \circ } = {Q_ \circ }w $
Here, $ {I_ \circ } $ , will be the amplitude current
 $ {Q_ \circ } $ , will be the charge
 $ w $ , will be the angular frequency
The charge is given by
 $ {Q_ \circ } = C{V_ \circ } $
Here, $ C $ will be the capacitor
Angular frequency is given by,
 $ w = \dfrac{1}{{\sqrt {LC} }} $ .

Complete step by step solution:
Here in this question we have to find the amplitude of the current. For this we have the values as a capacitor which is given as $ c = 10\mu F $ and similarly the resistor is given by $ R = 15\Omega $ .
So for solving, as we know that Impedance of current will be given by
 $ \Rightarrow {I_ \circ } = {Q_ \circ }w $
Now on substituting the value of charge which is given in the formula, we will get
 $ \Rightarrow {I_ \circ } = C{V_ \circ }w $
And from this angular frequency can also be written as
 $ \Rightarrow {I_ \circ } = C{V_ \circ } \times \dfrac{1}{{\sqrt {LC} }} $
On solving furthermore, we will get the equation as
 $ \Rightarrow {I_ \circ } = \sqrt {\dfrac{C}{L}} {V_ \circ } $
So now on substituting the values, we will get the equation as
 $ \Rightarrow {I_ \circ } = \sqrt {\dfrac{{10 \times {{10}^{ - 60}}}}{{10 \times {{10}^{ - 3}}}}} \times 20 $
Since the liker term will cancel each other so on solving it we will get the equation as
 $ \Rightarrow {I_ \circ } = 0.2\sqrt {10} A $
Therefore, the amplitude of the current will be $ 0.2\sqrt {10} A $ .
Hence, the option $ \left( A \right) $ is correct.

Note:
So an RC series circuit having both the capacitor and the resistor. And a capacitor can accumulate the energy and a resistor positioned in the series will switch the rate at which it charges or discharges. And the characteristic time dependence will be exponential.