Question

The switch in the figure below was closed for a long time. It is opened at t = 0. The current in the inductor of 2 H for t $\ge$ 0, is

• A. 2.5 $e^{-4t}$
• B. 5 $e^{-4t}$
• C. 2.5 $e^{-0.25t}$
• D. 5 $e^{-0.25t}$

Answer 1

The correct option is A 2.5 $e^{-4t}$

From the given circuit, consider the following circuit diagram,

For t $\ge$ 0:

$I_0=i\left(0^{-}\right)$

= 2.5 A

We can write,

$i\left(t\right)=I_0{e}^{\frac{-Rt}{L}}$

$i\left(t\right)=2.5e^{-4t}A$