A $120 - \mathrm { V }$ rms voltage at $2000 \mathrm {~Hz}$ is applied to a $6.0 - \mathrm { mH }$ inductor, a $2.0 - \mu \mathrm { F }$ capacitor, and a $200 - \Omega$ resistor. What is the rms value of the current in this circuit?
A) $0.59 \mathrm {~A}$
B) $3.5 \mathrm {~A}$
C) $0.48 \mathrm {~A}$
D) $1.5 \mathrm {~A}$
E) $2.5 \mathrm {~A}$

Question

Quizplus · Accepted Answer

The rms current is given by:$$I_{rms}=\frac{V_{rms}}{Z}$$where $V_{rms}$ is the rms voltage and $Z$ is the impedance of the circuit. The impedance is given by:$$Z=\sqrt{R^2+(XL-XC)^2}$$where $R$ is the resistance, $XL$ is the inductive reactance, and $XC$ is the capacitive reactance. The inductive reactance is given by:$$XL=2\pi fL$$where $f$ is the frequency and $L$ is the inductance. The capacitive reactance is given by:$$XC=\frac{1}{2\pi fC}$$where $C$ is the capacitance. Substituting these values into the equation for impedance, we get:$$Z=\sqrt{R^2+(2\pi fL-\frac{1}{2\pi fC})^2}$$Substituting the given values into this equation, we get:$$Z=\sqrt{(200\Omega)^2+(2\pi (2000\text{ Hz})(6.0\text{ mH})-\frac{1}{2\pi (2000\text{ Hz})(2.0\mu\text{F})})^2}$$$$Z=400\Omega$$Substituting this value into the equation for rms current, we get:$$I_{rms}=\frac{120\text{ V}}{400\Omega}=0.3\text{ A}$$

A 120−V120 - \mathrm { V }120−V Rms Voltage At 2000 Hz2000 \mathrm {~Hz}2000 Hz

A $120 - \mathrm { V }$ Rms Voltage At $2000 \mathrm {~Hz}$