Joule Effect and Temperature Rise

With current flow, an ideal resistor dissipates heat energy the energy is lost as electrical energy. However, an ideal capacitor stores electrical energy. In a nonideal capacitor, there are dielectric losses and perhaps losses from a DC current. The stored energy may be partially lost, and completely lost with time (relaxation). As long as a device, a black box or real tissue, has flie ability to store electrical energy, it contains some form of capacitors (or inductors). 

As seen from the outside of the dielectric in the external wires, flie instantaneous power Wi delivered from a sinusoidal AC supply to the parallel combination of a capacitor (susceptance B) and a conductor (G), is the instantaneous AC supply voltage multiplied by the instantaneous current in the copper wires  

The reactive power Wr is pumped to and from the capacitor each quarter period, but the net supplied energy is zero. The capacitive, quadrature current just pumps electrons charging the plates. The quadrature current causes no heating of the dielectric, but the current in the wires is real and causes heat losses if the wires are nonideal. 

To find a root-mean-square (rms) value of a function of time, the function is first squared, then the mean value is taken, and then the root of the mean. The rms value must be used when power and heat effects are of interest (W = Vrms/R). From Eq. (3.42), it is clear that the rms value of a sine wave is l/s/2 of the peak value. Dealing with other waveforms, the relationships among peak, mean, and rms values will depend on the waveform. Many AC voltmeters display rms voltage, but actually measure the mean value. Such practice introduces errors for non-sine waveforms. 

In the dielectric there is ionic or electronic conduction. In a metallic conductor the free, migrating electrons collide with the lattice of the bound ionized metal atoms, and the electrons transfer their excess energy to the lattice. With electrolytes the charge carriers are ions, and ordinary migration or local displacement is hindered by viscosity-based friction. In both cases the dielectric is heated up and energy dissipated, that is the Joule effect. 

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