An RLC circuit has a 400 ohm resistance a 2.5 mH inductor and a capacitor. If the circuit is in resonance at 30kHz and is attached to a 20mVrms power supply, what is the power dissipated by the circuit?
I'm assuming that the power supply is at the resonant frequency. Therefore, by definition, at resonance the series impedance of the inductor and capacitor equals zero. The power supply therefore sees just a 400 ohm resistor. Therefore the power dissipation is given by V^2/R, which equals 1 microwatt.
At resonance +jXL -jXC, therefore Z R +jXL -jXC R 400 ohms, since the reactances canel out. The power is only disspiated in the 400 ohm resistor, so P V^2 / R P (0.020V)^2 / 400 P 1E-6 Watt P 1 microWatt ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ EXTRA CREDIT The capacitor value for resonance with the 2.5 mH inductor at the frequency of 30 KHz will be f 1 / (2 * pi * SQRT (L * C) ) 30E3 Hz 1 / (2 * 3.1415 * SQRT (2.5E-3 H * C) ) 2 * 3.1415 * SQRT (2.5E-3 H * C) 1 / 30E3 Hz SQRT (2.5E-3 H * C) 5.3052E-6 (2.5E-3 H * C) (5.3052E-6)^2 2.5E-3 H * C 28.1448E-12 C 11.2579E-9 F C 0.0112579 microFarads (uF) 11.2579 nanoFarads (nF) 11,257.9 picoFarads (pF)
