In an LCR circuit as shown in figure, both switches are open initially. Now switch S1 is closed, S2 kept open. (q is charge on the capacitor and τ = RC is capacitive time constant). Which of the following statement is correct?
At t = , q = CV ( 1 e-1 )
Work done by the battery is half of the energy dissipated in the resistor
At t = τ, q = CV/2
At t = τ, q = CV ( 1 e-2 )
D.
At t = τ, q = CV ( 1 e-2 )
As switch S1 is closed and switch S2 is kept open. Now, capacitor is charging through a resistor R. Charge on a capacitor at any time t is
q = q0 ( 1 e-t/τ )
And q0 = CV
At t = ,
q = CV ( 1 e-t/2τ )
= CV ( 1 e-1/2 )
At t = τ
q = CV ( 1 e-τ/τ )
= CV ( 1 e-1 )
At t = 2τ
q = CV ( 1 e-2t /τ )
= CV ( 1 e-2 )
