You have a 0.400H inductor and a 6.00Fcapacitor. Suppose you take the inductor a

Question

You have a 0.400H inductor and a 6.00Fcapacitor. Suppose you take the inductor and capacitor and make a series circuit with a voltage source that has a voltage amplitude of 30.0V and an angular frequency of 250rad/s
A) What is the impedance of the curcuit?
B) What is the current amplitude?
C)What is the voltage amplitude across the capacitor.
D) What is the voltage amplitude across the inductor.
E) What is the phase angle
of the source voltage with respect to the current?

Please include all steps!

Explanation / Answer

a)

here

w = 250 rad/sec

Xl = w * L

Xl = 250 * 0.4 = 100 ohm

then

Xc = 1 / w*C

Xc = = 1 / 250 * 6*10^-6

Xc = 666.6 ohm

then

Z = mode of( Xl - Xc )

Z = mode of(100 - 666.6)

Z = 566.6 ohm

the impedance of the circuit is 566.6 ohm

b)

I = V / Z

I = 30 / 566.6

I = 0.0529 amp

the current of the circuit is 0.0529 amp

c)

Vc = I * Xc

Vc = 0.0529 * 666.6

Vc = 35.26 v

the voltage across capacitor is 35.26 v

d)

Vl = I * Xl

Vl = 0.0529 * 100

Vi = 5.29 v

the voltage across the inductor is 5.29 v

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