You have a 200 - omega resistor, a 0.400 - H inductor, and a 6.00 - muF capacito

Question

You have a 200 - omega resistor, a 0.400 - H inductor, and a 6.00 - muF capacitor. Suppose you take the resistor and inductor and make a series circuit with a voltage source that has voltage amplitude 30.0 V and an angular frequency of 250 rad/s. (a) What is the impedance of the circuit? (b) What is the current amplitude? (c) What are the voltage amplitudes across the resistor and across the inductor? (d) What is the phase angle phi of the source voltage with respect to the current? Does the source voltage lag or lead the current? (e) Construct the phasor diagram.

Explanation / Answer

Here ,

R = 200 Ohm

L = 0.400 H

C = 6 uF

a) impedance of the circuit , Z = R + j *(w*L - 1/(w*c))

Z = 200 + j *(0.4 * 250 - 1/(250 * 6 *10^-6))

Z = 200 - 567 j

Z = sqrt(200^2 + 567^2)

Z = 601.2 Ohm

the impedane of the circuit is 601.2 Ohm

b)

current = voltage /impedance

current amplitude = 30/601.2

current amplitude = 0.0499 A

the current amplitude is 0.0499 A

c)

voltage amplitude across resistor = 0.0499 * 200

voltage amplitude across resistor = 9.98 V

the voltage amplitude across resistor is 9.98 V

for the inductor

voltage amplitude across inductor = 250 * 0.40 * 0.0499

voltage amplitude across inductor = 4.99 V

the voltage amplitude across inductor is 4.99 V

d)

phase angle = arctan(-567/200)

phase angle = -70.6 degree

the phase angle is 70.6 degree and current is leading the source voltage

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