Question

In the circuit shows in Fig. the initail current through the inductor at `t = 0` is `I_(0)`. After a time `t = L//R`, the switch is quickly shifted to position 2.
a. Plot a graph showing the variation of current with time.
b. Calculate the value of current in the inductor at `t = (3)/(2) (L)/(R )`.

Answer 1

a. Shifting the position of switch increases the resistance of the circuit. This decreases the value of time constant.
Consequently, the rate of decreases of current increases.
The variation of current with tomes is shows in Fig
b.The equations of the curves are `i = I_(0)e^(-Rt//L)` (for `0 le t le L//R)`

For `(R )/(L) le t le oo` and `i = (0.37) I_(0)e^((-2R)/(L)(t-(L)/(R ))`
At `t = (3)/(2) (L)/(R )`, hence `i = (0.37) I_(0) e^((-2R)/(L)((3L)/(2R) - (L)/(R)))` or `i = (0.37)^(2) I_(0)`