∫ sin ω L t ω ω cos + constant The integration constant in the above equation is independent of time. Since the voltage in the circuit has only time dependent part, we can take the time independent part in the current (integration constant) as zero. the applied voltage and the current are in phase with each other in a resistive circuit. It means that they reach their maxima and minima simultaneously.
This is indicated in the phasor diagram (Figure . ). The wave diagram also depicts that current is in phase with the applied voltage (Figure . ).
. . AC circuit containing only an inductor Consider a circuit containing a pure inductor of inductance L connected across an alternating voltage source (Figure . ).
The instantaneous value of the alternating voltage is given by V m sin t t t I m sin ( t) OA = V m OB = I m v v v Figure . Phasor diagram and wave diagram for AC circuit with R Figure . AC circuit with inductor L v = V m sin t 12th - 12th - - - - - Unit ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENT offered by the inductor, called inductive reactance ( X L ). It is measured in ohm.
X L L = ω An inductor blocks AC but it allows DC. Why? and How? An inductor L is a closely wound helical coil.
The steady DC current flowing through L produces uniform magnetic field around it and the magnetic flux linked remains constant. Therefore there is no self-induction and self-induced emf (back emf). Since inductor behaves like a resistor, DC flows through an inductor. The AC flowing through L produces time-varying magnetic field which in turn induces self-induced emf (back emf).
This back emf, according to Lenz’s law, opposes any change in the current. Since AC varies both in magnitude and direction, its flow is opposed in L . For an ideal inductor of zero ohmic resistance, the back emf is equal and opposite to the applied emf. Therefore L blocks