A 120-V rms voltage is applied across a 6.0-μF capacitor and a series combination of a 100-Ω resistor.If the frequency of the power source is 60 Hz,what is the rms value of the current in the circuit?
A)0.26 A
B)0.36 A
C)0.46 A
D)0.56 A
E)0.76 A

Question

Quizplus · Accepted Answer

The rms current in the circuit is given by:$$I_{rms}=\frac{V_{rms}}{Z}$$where:* $$V_{rms}$$ is the rms voltage across the circuit* $$Z$$ is the impedance of the circuitThe impedance of the circuit is given by:$$Z=\sqrt{R^2+X_C^2}$$where:* $$R$$ is the resistance of the resistor* $$X_C$$ is the capacitive reactance of the capacitorThe capacitive reactance is given by:$$X_C=\frac{1}{2\pi fC}$$where:* $$f$$ is the frequency of the power source* $$C$$ is the capacitance of the capacitorSubstituting the given values into the equations above, we get:$$Z=\sqrt{100^2+\left(\frac{1}{2\pi (60)(6.0	imes10^{-6})}ight)^2}=100.5\Omega$$$$I_{rms}=\frac{120	ext{ V}}{100.5\Omega}=1.19	ext{ A}$$Therefore, the rms value of the current in the circuit is 1.19 A.

A 120-V Rms Voltage Is Applied Across a 6