31. Alternating Current

In an AC circuit, a resistor of $R$ is connected between points a and b. What is the equivalent resistance between points a and b?

In a plasma globe, a hollow glass sphere is filled with low-pressure gas and a small spherical metal electrode is located at its center. Assume an ac voltage source of peak voltage V_o and frequency f is applied between the metal sphere and the ground, and that a person is touching the outer surface of the globe with a fingertip, whose approximate area is 1.0 cm². The equivalent circuit for this situation is shown in Fig. 30–36, where R_G and R_P are the resistances of the gas and the person, respectively, and C is the capacitance formed by the gas, glass, and finger. (a) Determine C assuming it is a parallel-plate capacitor. The conductive gas and the person’s fingertip form the opposing plates of area A = 1.0 cm². The plates are separated by glass (dielectric constant K = 5.0) of thickness d = 2.0 mm. (b) In a typical plasma globe, f = 12 kHz. Determine the reactance X_C of C at this frequency in MΩ. (c) The voltage may be V_o = 2500 V. With this high voltage, the dielectric strength of the gas is exceeded and the gas becomes ionized. In this “plasma” state, the gas emits light (“sparks”) and is highly conductive so that R_G << X_C. Assuming also that R_P << X_C, estimate the peak current that flows in the given circuit. Is this level of current dangerous? (d) If the plasma globe operated at f = 1.0 MHz, estimate the peak current that would flow in the given circuit. Is this level of current dangerous?

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The voltage across a resistor is found to be given by v _R (t) = (10 V) cos[(120 s⁻¹)t]: 

a) At what frequency does the AC course operate? 

b) If the resistance is 12 Ω, what is the maximum current in this circuit? 

c) What is the RMS voltage of the AC source?

Calculate the peak current in a 2.5-k Ω resistor connected to a 220-V rms ac source.