The two capacitors, shown in the circuit, are initially uncharged and the cell is ideal.The switch S is closed at t = 0.

Which of the following functions represents the current i(t), through the cell as a function of time?Here `i_(0), i_(1), i_(2)` are constants.

Options

A. `i(t) = i_(0) + i_(1)e^(-t/tau), tau = 3C xx (R)/(3)`
B. `i(t) = i_(0) + i_(1)e^(-t/tau)+ i_(2)e^(-t/2tau), tau = RC`
C. `i(t) = i_(1) + i_(1)e^(-t/tau), tau = 3C xx (R)/(3)`
D. `i(t) = i_(0) + i_(1)e^(-t/tau), tau = 3RC`

Answer

B

Explanation

The three branches of the circuits carry currents `i = i_(0), i = i_(1) e^(t/RC)` and `i = i_(2) 2e^(-t/2RC)` respectively. The current through the cell, i() can be found by using Kirchhoff.s current law (or mode law).