A capacitor, a coil, and two resistors of equal resistance are arranged in an AC

Question

A capacitor, a coil, and two resistors of equal resistance are arranged in an AC circuit as shown in the figure below. An AC source provides an emf of DeltaV_rms = 14.5 V at a frequency of 60.0 Hz. When the double-throw switch S is open as shown in the figure, the rms current is 190 mA. When the switch is closed in position a, the rms current is 294 mA. When the switch is closed in position b, the rms current is 137 mA. (a) Determine the possible values of R. (Enter your answers from smallest to largest. Enter NONE in any unused answer blanks.) ohm ohm (b) Determine the possible values of C. (Enter your answers from smallest to largest. Enter NONE in any unused answer blanks.) muF (c) Determine the possible values of L. (Enter your answers from smallest to largest. Enter NONE in any unused answer blanks.) mH mH

Explanation / Answer

(b)
Z = sqrt(67.25^2 + (1/(2**60*X))^2)

Vrms = Irms * Z
14.5 = 137 * 10^-3 * sqrt(67.25^2 + (1/(2**60*X))^2)
C = 3.25 * 10^-5 F
C = 32.5 uF

(c)
Now,
Z = sqrt(67.25^2 + [(2**60*L) - 1/(2**60*32.5*10^-6)]^2)

Vrms = Irms * Z
14.5 = 190 * 10^-3 * sqrt(67.25^2 + [(2**60*L) - 1/(2**60*32.5*10^-6)]^2)
L = 0.1208 H = 120.8 mH
L = 0.3122 H = 312.2 mH

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