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 = (4.00 V)cos[(755 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

In a series RL circuit, the current through the inductor will be the same as that through the resistor. We are given the voltage across the resistor. The current through the resistor, and through the inductor as well, will be given by the expression
I = V_R / R

I = ( 4 V ) cos[(755 rad/s) t ] / 150

I = 0.0267 cos[(755 rad/s) t )] amp

b)

Xl = w * L

Xl = 755 * 0.250 = 188.75 ohm

so the inductive reactance of the inductor is 188.75 ohm

c)

The voltage across the inductor will then be
VL = L*dI/dt

VL= 0.250 * d[ 4 * cos (755t) / 150] / dt

VL= 0.250 / 150 * 4 * d[cos (755 t)]/dt

VL= 0.250/150 * 4 *(-755)sin (755t)

VL= -5.034 sin (755t) V

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