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Prove that in a pure resistive circuit t...

Prove that in a pure resistive circuit the current is in phase with the applied voltage.

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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
`upsilon=V_(m)=sin omegat" ...(1)"`
An alternating current i flowing in the circuit due to this voltage, develops a potential drop across R and is given by
`V_(R)=iR" ....(1)"`
Kirchhoff .s loop rule states that the algebraic sum of potential differences in a closed circuit is zero. For this resistive circuit,
`upsilon-V_(R)=0`
From equation (1) and (2),
`V_(m)sin omega t=iR`
`i=(V_(m))/(R ) sin omegat`
`i=I_(m) sin omegat" ...(3)"`
where `(V_(m))/(R )=I_(m),` the peak value of alternating current in the circuit, From equations (1) 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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