# Instantaneous current value in AC circuit

• Engineering
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} ##

## 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?

Homework Helper
Gold Member

## 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} ##

## 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.