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shivakumar
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how does capacitors and inductors cause phase difference between current and voltage? how does complex number come into play to explain the relation between phase of current and voltage?
It may be worth while pointing out that there is only a phase shift because of the finite resistances in a circuit. If you connect a capacitor across an AC voltage source (i.e. zero source resistance) the current flowing into the Capacitor will be totally in phase with the volts.shivakumar said:how does capacitors and inductors cause phase difference between current and voltage?
No. The capacitor current is shifted wrt the voltage by 90^{o} because ##~i=C\frac{dv}{dt}~##.sophiecentaur said:If you connect a capacitor across an AC voltage source (i.e. zero source resistance) the current flowing into the Capacitor will be totally in phase with the volts.
Whoops - you're right. q = Cv so differentiate both sides. . . . .DaveE said:No. The capacitor current is shifted wrt the voltage by 90o because i=Cdvdt .
If you set ##R=0## in my treatment of the RC-series circuit you get ##\varphi=\pi/2##, i.e., the current is by 90 degrees advanced compared to the voltage (in the stationary state of course).sophiecentaur said:It may be worth while pointing out that there is only a phase shift because of the finite resistances in a circuit. If you connect a capacitor across an AC voltage source (i.e. zero source resistance) the current flowing into the Capacitor will be totally in phase with the volts.
When a series R is added, there is a finite time lag between the supply voltage and the instantaneous charge in the capacitor.
The denominator on the right side should be under a square root.vanhees71 said:To get the phase shift between current and voltage you have to write the prefactor in "polar form". The modulus is
$$\left | \frac{U_0 C \omega (\omega R C+\mathrm{i})}{1+\omega^2 R^2 C^2} \right|=\frac{U_0 \omega C}{1+\omega^2 R^2 C^2},$$
Phase difference in electricity refers to the difference in the timing of the peaks and troughs of two alternating currents or voltages. It is measured in degrees or radians and represents the shift in the waveforms of the two signals.
Capacitors and inductors are two types of reactive components in electrical circuits. They store energy in the form of electric and magnetic fields, respectively. When an alternating current flows through these components, the phase difference between the current and voltage depends on the frequency and the values of capacitance and inductance.
In electrical engineering, complex numbers are used to represent the magnitude and phase of an alternating current or voltage. The real part of a complex number represents the magnitude, while the imaginary part represents the phase. By using complex numbers, we can easily perform calculations involving phase differences.
The phase difference between current and voltage affects the impedance (resistance to the flow of current) of capacitors and inductors. At certain frequencies, the impedance of these components can be either higher or lower due to the phase difference, which can affect the overall behavior of the circuit.
No, phase difference is a concept that is only applicable to alternating current circuits. In DC circuits, the current and voltage remain constant and do not alternate, so there is no concept of phase difference.