The current in a coil with a self-inductance of 1 mH is 2.8 A at t = 0, when the coil is shorted through a resistor. The total resistance of the coil plus the resistor is 11.0 capital omega. (a) Find the current in the circuit after 0.5 ms.

Respuesta :

Given:

L = 1 mH = [tex]1\times 10^{-3}[/tex] H

total Resistance, R = 11 [tex]\Omega[/tex]

current at t = 0 s,

[tex]I_{o}[/tex] = 2.8 A

Formula used:

[tex]I = I_{o}\times e^-{\frac{R}{L}t}[/tex]

Solution:

Using the given formula:

current after t = 0.5 ms = [tex]0.5\times 10^{-3} s[/tex]

for the inductive circuit:

[tex]I = 2.8\times e^-{\frac{11}{1\times 10^{-3}}\times 0.5\times 10^{-3}}[/tex]

[tex]I =   2.8\times e^-5.5[/tex]

I =0.011 A