A 150- resistor is connected in series with a 0.250-H inductor. The voltage acro

Question

A 150- resistor is connected in series with a 0.250-H inductor. The voltage across the resistor is

vR = (9.25 V)cos[(740 rad/s)t].

(a) Derive an expression for the circuit current. (Assume the frequency is in rad/s. Do not include units in your expression. Use the following as necessary: t.)
IL(t) =   A

(b) Determine the inductive reactance of the inductor.
XC =  

(c) Derive an expression for the voltage VL across the inductor. (Assume the frequency is in rad/s and all other values are in MKS. Do not include units in your expression. Use the following as necessary: t.)
vL(t) =   V

Explanation / Answer

a)

by using the formula

I = E /Z

Z = sqrt( R^2 + (Xl - Xc)^2) = sqrt( R^2 + Xl^2)

Z = sqrt( R^2 + (w * L)^2 )

I = E / sqrt( R^2 + (wL)^2)

I = 9.25 / sqrt(150^2 + (0.25)^2) = 0.0616 amp

i = 0.0616 * cos(740t)

i = (0.0616 A ) cos((740 rad/s) t)

b)

Xl = w * L

Xl = 740 * 0.25 = 185 ohm

c)

Vl = L * dl/dt

= 0.25 * d(9.25 * cos(740t) /150) /dt

= 0.25/150 * 9.25 * (-740) * ( sin(740t)) /dt

= -11.4 sin( 740t) volts

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