Engineering Instantaneous current value in AC circuit

[Raghav Gupta]

Homework Statement

A sinusoidal supply defined by $v(t)= 325.27 sin(314.16t+\frac{\pi}{6})$ is connected
across a coil of resistance 25Ω and inductance of 0.5 H. The instantaneous value of the current at 2.968ms is
13.13 mA
21.6 mA
87.8mA
13.8mA

Homework Equations

$i(t) = \frac{v(t)}{Z}$ where Z is impedance
$Z= \sqrt{R^2 + ω^2L^2}$
$ω= 314.16 radian/s$

The Attempt at a Solution

$i(t) = \frac{v(t)}{Z}$
Substituting all values getting,
2.0315 A which is not matching with any of the options.
What is wrong here?

 

[cnh1995]

Homework Statement

A sinusoidal supply defined by $v(t)= 325.27 sin(314.16t+\frac{\pi}{6})$ is connected
across a coil of resistance 25Ω and inductance of 0.5 H. The instantaneous value of the current at 2.968ms is
13.13 mA
21.6 mA
87.8mA
13.8mA

Homework Equations

$i(t) = \frac{v(t)}{Z}$ where Z is impedance
$Z= \sqrt{R^2 + ω^2L^2}$
$ω= 314.16 radian/s$

The Attempt at a Solution

$i(t) = \frac{v(t)}{Z}$
Substituting all values getting,
2.0315 A which is not matching with any of the options.
What is wrong here?

If I'm not wrong, t=2.968ms is the time elapsed after the circuit was switched on. I think you should go for transient response. Your calculations are correct, but they are for the steady state. 2.031A is the peak current. Time constant of your cicruit is 20ms.

 

[Svein]

Substituting all values getting,
2.0315 A which is not matching with any of the options.
What is wrong here?

When looking for the instantaneous current, you need to consider the phase angle of the impedance. Subtract that phase angle from the v(t) phase and you will get an answer that matches one of your options.