Here, the ac voltage supply is that is applied across the inductor.
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is peak voltage of the ac supply and is the frequency of the ac voltage.
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The current through the inductor varies and opposing induced emf is generated in the inductor.
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So, the induced emf: .............
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By applying Kirchoff's law in the above circuit, we get:
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.............
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By integrating both side, we get the instantaneous value of current:
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.............
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So, the peak current is
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Now, using equation we get: .............
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Hence, in inductor the current lags behind the voltage by a phase angle of .
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The average power dissipated across the inductor will be: ...............
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Here, is the phase difference between voltage and current at an instant that is , by substituting this in we get:
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Hence, the power dissipated across the inductor is zero.
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The phasor diagram for the given circuit:
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Embibe Experts Physics Solutions for Exercise - Embibe Experts Solutions for Chapter: Alternating Current, Exercise 1: Goa Board-2018
Attempt the free practice questions on Chapter 7: Alternating Current, Exercise 1: Goa Board-2018 with hints and solutions to strengthen your understanding. EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS solutions are prepared by Experienced Embibe Experts.
Questions from Embibe Experts Solutions for Chapter: Alternating Current, Exercise 1: Goa Board-2018 with Hints & Solutions
For a purely inductive ac circuit, show that the current lags the voltage by a phase angle of radians. Hence, show that the power dissipated across the inductor is zero. Draw the phasor diagram.
LCR series circuit is connected to an ac source of voltage . Using phasor diagrams, obtain an expression for the impedance and the phase angle between the voltage and the current.
In an Indian laboratory, a circuit running on low AC voltage is connected to the AC mains through an electrical device .If the electrical device is 100% efficient, state whether its input current will be greater or less than the output current.
Show that the voltage and current are always in phase when a resistance is connected across an A.C. source. Draw the phasor diagram for it. To tune a radio over a frequency range of , inductance ‘L’ is kept constant and the corresponding capacitance is varied from . Compare .