15.4 Power in an AC Circuit

An ac voltmeter attached across the terminals of a 45-Hz ac generator reads 7.07 V. Write an expression for the emf of the generator.

Show that the rms voltages across a resistor, a capacitor, and an inductor in an ac circuit where the rms current is $I_{\text{rms}}$ are given by $I_{\text{rms}} R , I_{\text{rms}} X_{C} , \text{and} I_{\text{rms}} X_{L} ,$ respectively. Determine these values for the components of the RLC circuit of the equation.

Discuss the differences between average power and instantaneous power.

Can the instantaneous power output of an ac source ever be negative? Can the average power output be negative?

Calculate the rms currents for an ac source is given by $v \left(t\right) = V_{0} \text{sin} \omega t ,$ where $V_{0} = 100 \text{V}$ and $\omega = 200 \pi \text{rad}/\text{s}$ when connected across (a) a $20 - \mu \text{F}$ capacitor, (b) a 20-mH inductor, and (c) a $50 - \Omega$ resistor.

For an RLC series circuit, the voltage amplitude and frequency of the source are 100 V and 500 Hz, respectively; $R = 500 \Omega$; and $L = 0.20 \text{H}$. Find the average power dissipated in the resistor for the following values for the capacitance: (a) $C = 2.0 \mu \text{F}$ and (b) $C = 0.20 \mu \text{F} .$

An RLC series circuit has an impedance of $60 \Omega$ and a power factor of 0.50, with the voltage lagging the current. (a) Should a capacitor or an inductor be placed in series with the elements to raise the power factor of the circuit? (b) What is the value of the reactance across the inductor that will raise the power factor to unity?