1.

Initially the switch 'S' is open for a ling time. Now the switch 'S' is closed at t=0(R_(1)=2Omega, R_(2)=2Omega, C_(1)=1F and C_(2)=1F) Then

Answer»

The current through the WIRE `AB` at `t=2` sec is `1//2e` ampere
The current through the wire at `t=2` sec is `1//e` ampere.
The charge on the CAPACITOR `C_(2)`, which has INITIALLY unchargd at `t=2` sec is `(1- 1/(2e))` coulimbs
The charge on the capacitor `C_(1)` at `t=2` sec is `(1- 1/(2e))` coulombs

Solution :
When the switch is closed then at `t=0` the distribution of the charge is shown in the figure.

By applying Kirchooff's Law `I_(1)^(')=((1-q))/2`
`int_(1//2)^(q) (dq)/(1-q)=int_(0)^(1) (dt)/2`
`q=(1-1/2e^(-t//2))`
`I_(1)^(')=(dq)/(dt)=1/4 e^(-t//2)`


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