- #1

- 139

- 0

## Homework Statement

Use Laplace transforms to derive an expression for the current flowing in the circuit shown in the figure, given that i = 0 when t=0

## Homework Equations

Expression for the current in an LR series circuit

I(t) = V / R (1-e-Rt/L)

V - Volts (6V)

R - Ohms (10Ω)

L - Henries (2H)

t - Seconds

e - The base of the Natural Logarithm = 2.71828

Steady State Current

I = V / R

I = 6 / 10

I = 0.6 A

Time Constant

τ = L / R

τ = 2 / 10

τ = 0.2 seconds

Instantaneous Current

I(t) = Vs / R (1 - e-Rt/L)

I(t) = 6 / 10 (1 - e-10x0.2/2)

I(t) = 6 / 10 (1 - e-2/2)

I(t) = 6 / 10 (1 - 0.36787)

I(t) = 0.6 (0.63213)

I(t) = 0.379

I(t) = 0.38 A