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A resistor and inductor are connected in series across an ac generator. The voltage of the generator is given by V ( t ) = V 0 cos ( ω t ) , where V 0 = 120 V , ω = 120 π rad / s , R = 450 Ω , and L = 8.5 H . (a) What is the magnitude of the impedance of the L R circuit? (b) What is the amplitude of the current through the resistor? (c) What is the phase difference between the voltage and current?

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Answer:

Explanation:

Vo = 120 V

ω = 120π rad/s

R = 450 ohm

L = 8.5 H

(a)

XL = ω L = 120 x 3.14 x 8.5 = 3202.8 ohm

Impedance is given by

[tex]Z=\sqrt{R^{2}+X_{L}^{2}}[/tex]

[tex]Z=\sqrt{450^{2}+3202.8^{2}}[/tex]

Z = 3234.26 ohm

(b) Io = Vo / Z

Io = 120 / 3234.26 = 0.037 A

(c) Phase is given by

[tex]tan \phi = \frac{X_{L}}{R}[/tex]

tan Ф = 3202.8 / 450

tan Ф = 7.117

Ф = 82°

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