You have a 150- resistor and a 0.420-H inductor. Suppose you take the resistor a

Question

You have a 150- resistor and a 0.420-H inductor. Suppose you take the resistor and inductor and make a series circuit with a voltage source that has a voltage amplitude of 33.0 V and an angular frequency of 280 rad/s .

A) What is the impedance of the circuit?

B) What is the current amplitude?

C) What is the voltage amplitude across the resistor?

D) What is the voltage amplitudes across the inductor?

E) What is the phase angle of the source voltage with respect to the current?

F) Does the source voltage lag or lead the current?

G) Construct the phasor diagram.

Explanation / Answer

A)

Voltage source is E = (33.0V)sin280t

where = 280 rad/s

So reactance of the inductor is,

XL = L = 0.42HX280rad/s = 117.6

So impedance of the circuit is,

Z = [R2 + XL2] =  [(150)2 + (117.6)2]

or, Z = 190.6

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B)

Current amlitude is,

Ip = Vp/Z = 33V/(190.6)

or, Ip = 0.173 A

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C)

Voltage amplitude across the resistor is,

Vpr = IpR = (0.173 A)(150 )

or, Vpr = 26V

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D)

Voltage amplitude across the inductor is,

VpL = IpXL = (0.173 A)(117.6)

or, VpL = 20.36 V

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E)

we have tan = -XL/R = -117.6/150

or, = -380 is the angle of current with respect to the source voltage

So, the phase angle of source voltage with respect to current is = 380

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F)

The source voltage leads the current.

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This concludes the answers. Check the answer and let me know if it's correct. If you need any more clarification or correction, feel free to ask.....

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