Solved: In a plasma globe, a hollow glass sphere is filled

Chapter , Problem 96

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In a plasma globe, a hollow glass sphere is filled withlow-pressure gas and a small spherical metal electrode islocated at its center. Assume an ac voltage source of peakvoltage V0 and frequency / is applied between the metalsphere and the ground, and that a person is touchingthe outer surface of the globe with a fingertip, whoseapproximate area is 1.0 cm2. The equivalent circuit for thissituation is shown in Fig. 30-35, where R G and R P are theresistances of the gas and the person, respectively, and Cis the capacitance formed by the gas, glass, and finger.(a) Determine C assuming it is a parallel-plate capacitor. Theconductive gas and the persons fingertip form the opposingplates of area A = 1.0 cm2. The plates are separated byglass (dielectric constant K = 5.0) of thicknessd = 2.0 mm. (b ) In a typical plasma globe, / = 12 kHz.Determine the reactance X c of C at this frequency in M ft.(c) The voltage may be Vq = 2500 V. With this highvoltage, the dielectric strength of the gas is exceeded andthe gas becomes ionized. In this plasma state, the gasemits light ( sparks ) and is highly conductive so thatR q X c . Assuming also that R P X c , estimate thepeak current that flows in the given circuit. Is this level ofcurrent dangerous? (d) If the plasma globe operated at/ = 1.0 MHz, estimatethe peak current thatwould flow in the givencircuit. Is this level of Lowcurrentdangerous?