A 25.0-mH inductor, a 2.00-μF capacitor, and a certain resistor are connected in series across an ac voltage source at 1000 Hz. If the impedance of this circuit is 200 Ω, what is the value of the resistor? a. 200 Ω b. 552 Ω c. 184 Ω d. 100 Ω e. 579 Ω
Z sqrt [(Xl - Xc)^2 + R^2] w 1000*2*pi 6280 Xl Lw 157 ohms Xc 1/(C*6280) 79.61 ohms so 200 sqrt[(157 - 79.61)^2 + R^2] on solving we get R 184 ohms
25 mH Inductor 0.025 H inductor Xl 2 * pi * freq * L j157.0796 2.0uF Capacitor Xc 1 / (2 * pi * freq * C) -j79.5775 Xl + Xc j77.5022 77.5022 @ 90 degrees Since Z^2 R^2 + X^2 Z SQRT ( R^2 + (Xl - Xc)^2 ) with the total impedance as 200 ohms, the resistor is 200 SQRT ( R - 77.5022) 184.3730 ohms (b) 184 ohms
