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| AC Circuit Containing Pure Inductance only |
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| Let an AC source be connected across a pure inductive element. If the alternating current I = Io sin wt flows through it. Then |
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| According to Kirchhoff's Law |
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| E = Eo cos wt |
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| or |
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| where Eo = LWIo |
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| Here Eo = LwIo. This is similar to E = IR. Therefore, Lw plays the same role as that of a resistor. The inductor impedes the flow of alternating current in the circuit. |
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| Therefore, the non-resistant opposition of a coil to alternating current due to the varying magnetic field is called inductive reactance of the coil XL. |
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| Unit of XL is also ohm (W) |
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| The inductive reactance |
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| XL = WL = 2pfL |
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| Note: |
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| To have a large reactance the coil |
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(i) Should have many turn as L  N. |
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(ii) Should have an iron-core as L  mrmo . |
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| (iii) Also the frequency of a.c should be high. |
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| Therefore, XL in case of DC (direct current), is zero. |
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| The relation between XL and f is a straight line. |
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| The EMF E is found to lead the current by 90o. Therefore, the phasor diagram will be |
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| The arrow in the anticlockwise direction indicates E leads I by 90o. |
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| The sinusoidal variation can also be represented as |
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| The alternating EMF across an inductor attains the maximum value well before the current attains its maximum value, and hence we say leads I by 90 or p/2. |
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| If we have two long, rigid parallel wires carrying current in the same direction, then the two wires experience a force of attraction. |
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| Therefore work has to be done in separating them and this work done is stored in the magnetic field surrounding the wires. One can recover that additional stored magnetic energy by letting the wires move back to their original position, as it is the most stable position for the system. |
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| We regard energy as stored in the magnetic field of an isolated wire, in analogy with the energy of the electric field of an isolated charge. In the following case, the total stored magnetic energy in an inductance L carrying a current I is as follows. |
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| When AC is applied to an inductor of inductance L, the current in it grows from zero to the maximum steady value Io. If I is the current at any instant t, then the induced EMF developed in the inductor at that instant is |
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| Negative sign indicates that induced EMF opposes any change in current. To maintain the current, the external source should do some work for which |
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| Therefore, in small time dt, the work done will be: |
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| where Io represents the maximum value of current. |
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| Therefore this is the energy stored in the inductor. |
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