Answer:
C) [tex]12.3 [/tex] volts
Explanation:
f = frequency of oscillator = 1 kHz = 1000 Hz
[tex]V_{rms}[/tex] = 12 Volts
L = Inductance of Inductor = 5 mH = 0.005 H
[tex]X_{L}[/tex] = Inductive reactance
Inductive reactance is given as
[tex]X_{L}[/tex] = [tex]2\pi fL[/tex]
[tex]X_{L}[/tex] = [tex]2(3.14) (1000)(0.005)[/tex]
[tex]X_{L} = 31.4 [/tex]
[tex]X_{C}[/tex] = Capacitive reactance
Capacitive reactance is given as
[tex]X_{C}=\frac{1}{2\pi fC}[/tex]
[tex]X_{C}=\frac{1}{2(3.14)(1000)(4\times 10^{-6})}[/tex]
[tex]X_{C} = 39.8 [/tex]
Impedance of the circuit is given as
[tex]z = \sqrt{R^{2}+(X_{L} - X_{C})^{2}}[/tex]
[tex]z = \sqrt{102^{2}+(31.4 - 39.8)^{2}}[/tex]
[tex]z = 102.35 [/tex]
Rms Current flowing is given as
[tex]i = \frac{V_{rms}}{z}[/tex]
[tex]i = \frac{12}{102.35}[/tex]
[tex]i = 0.12[/tex] A
Rms potential difference across the resistor is given as
[tex]V = i R [/tex]
[tex]V = (0.12) (102) [/tex]
[tex]V = 12.3 [/tex] volts
