Phase angle applied voltage

Reorientation of dipoles in the direction of the field is characterized by a relaxation time, T. When t is small compared to the frequency of the applied voltage, instantaneous polarization occurs when t is large, the resultant polarization will be free from orientational contribution. A dispersion of polarization and hence of e, occurs when the frequency and t are close to each other and e, in this region is a complex quantity, — i . In the region of dispersion there is a phase lag between the applied field and the instantaneous polarization when the phase angle 5 is small, tan 5 = eJe,. Furthermore,... 

Although not dealt with in this chapter, AC impedance measurements (sometimes called electrochemical impedance spectroscopy) are important in studying electrode dynamics. Generally in this method, a sinusoidal voltage (10 2 to 105 Hz) is applied to the cell, the phase angle and the amplitude of the response current are measured as a function of... 

The current and voltage are exactly in phase, and therefore, the phase angle of the current relative to the voltage, 0, is zero. Next, consider the capacitor, where the same ac voltage, V, is applied at the same frequency, cOj. The capacitance, C, is given by ... 

Figure 19. Peak faradaic admittance spectra for Cd2+/Cd(Hg) system after nonfaradaic compensation. System DME-aqueous 1.0 M ZnS04, 0.18 M H2SO4 at 25°C. Applied Pseudo-random odd-harmonic a.c. waveform with 1.5 mV per frequency component, 26 components superimposed on d.c. voltage of 0.523 volt vs. Ag/AgCl (saturated NaCl). Measured Average of 10 replicates at 3.0 s in life of mechanically controlled drop life. A = phase angle cotangent. B = total admittance spectrum.

When circuits contain two or more separate elements, such as RL, RC or RLC, the phase angle between the total voltage and total current will be neither 0° nor 90° but will be determined by the relative values of resistance and reactance in the circuit. In Fig. 2.37 the phase angle between applied voltage and current is some angle 4>. 

Dielectric phase angle n. The angular difference in phase between the alternating voltage (usually sinusoidal) applied to a dielectric and the resulting current. The angle is often symbolized by 9, the cosine of which is the power factor. Ku CC, Liepins R (1987) Electrical properties of polymers. Hanser Publishers, New York. 

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