Oliver Heaviside (1850 - 1925), pioneer in the analysis of AC circuits!
ALTERNATING CURRENT CIRCUITS

AC circuit with only resistance. (Voltage and current are in step)

 

AC circuit with only capacitance. Current is ahead of voltage.

AC circuit with only inductance. Current is behind voltage.


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We have mentioned several times that an LC circuit has the same differential equation as an undamped harmonic oscillator... Q and I oscillate harmonically.

An LRC circuit can behave like a damped harmonic oscillator. The differential equation has three different types of solutions, overdamped, critically damped, and underdamped.  We will only consider one of the three possible cases, the case of underdamped oscillations. In circuits, this is sometimes called “ringing.” In such a case, the frequency of oscillation is:

















The average power is the average over one cycle of Ip sin[ω t - φ] Vp sin[ω t],
 or of the equivalent expression, Ip sin[ω t ] Vp sin[ω t + φ].



Some worked AC circuit examples!

Still more worked AC circuit examples!


Maxwell realized Ampere's Law leads to a paradox unless there is another term besides the current enclosed by a path. The possibility of a time-varying electric field enclosed by the surface that the path is the boundary of would also lead to a magnetic field.



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