A 5.03 H inductor with negligible resistance is connected across an ac source whose voltage amplitude is kept constant at 58.0 V but whose frequency can be varied.Find the current amplitude when the angular frequency is 104 rad/s.I really don't know how H turns into F but i know that the units must coalese somehow.Whenever i try to multiply this out i get an answer that is not in Amps.I know the equation (at least the one i use)is IV*omega*C The only problem is that i don't know how to get C from the inductor value.Please help if you can, any will be appreciated.Sincerely,PhysicsDisciple
The reactance of a capacitor is Xc -1/(ωC), whereas the reactance of an inductor is X? ωL The impedance of these devices, when expressed as a complex number, is Z R + jX, where j √-1 and the current is given by the formula I V/Z For a capacitor, this would be I V / (-j/(ωC)) jVωC, which, except for the j term, is what you would have expected. The ratio of the pure and imaginary terms gives the phase of the current with respect to the voltage. If the voltage is positive real and the current is positive pure imaginary, the current will lead the voltage by 90 degrees. On the other hand, for an inductor, I V / (jωL) -jV/(ωL) The negative pure imaginary current indicates that the current lags the voltage by 90 degrees and the magnitude will be Io Vo/(ωL) In this example, Io 58.0 volts / (104 s^-1 * 5.03 H) 0.111 A
