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in Electromagnetic Induction and Alternating Current by (48.5k points)
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Find out the phase relationship between voltage and current in a pure resister circuit.

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AC circuit containing pure resistor: 

Consider a circuit containing a pure resistor of resistance R connected across an alternating voltage source. The instantaneous value of the alternating voltage is given by

υ = Vm sin ωt ….. (1) 

An alternating current i flowing in the circuit due to this voltage, develops a potential drop across R and is given by

VR = iR ……. (2)

Kirchoff’s loop rule states that the algebraic sum of potential differences in a closed circuit is zero. For this resistive circuit,

υ – VR = 0

From equation (1) and (2),

Vm sin ωt = iR

⇒ i =\(\frac{V_m}{R}\) sin ωt

i = Im sin ωt …… (3)

where \(V\frac{V_m}{R}\) = Ithe peak value of alternating current in the circuit. From equations (1) and and (3), it is clear that 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. The wave diagram also depicts that current is in phase with the applied voltage.

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