Answer: 17.6 ohm.
- A 10 ohm
- B 17.6 ohm
- C 31.4 ohm
- D 41.5 ohm
Correct answer: B. 17.6 ohm
Explanation: XL = 2 pi x 50 x 0.1 = 31.4 ohm. XC = 1/(2pi x 50 x 10<sup>-4</sup>) = 31.8 ohm. Z = sqrt(100 + (31.4-31.8)<sup>2</sup>) = sqrt(100 + 0.16) = approx 10.008 ohm. Basically 10 ohm at near-resonance.
In a pure inductor the current lags the voltage by 90° (energy is briefly stored in the magnetic field before current responds); in a pure capacitor the current leads the voltage by 90° (current must flow to build up charge before voltage rises) - the mnemonic "ELI the ICE man" keeps these straight.
Concept context
AC circuits, impedance, LCR series circuit, resonance, transformers, and power factor.