Question

# A circuit contains a resistance R and an inductance L in series. An alternating voltage V=V0sinωt is applied across it. The currents in R and L respectively will be (I0 is the peak current)

A
IR=I0cosωt, IL=I0cosωt
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B
IR=I0sinωt, IL=I0cosωt
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C
IR=I0sinωt, IL=I0cosωt
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D
IR=IL=I0sinωt
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Solution

## The correct option is D IR=IL=I0sinωtPhasor diagram for resistor and inductor, shown below: For resistance R, voltage and current has the same phase. ∴IR=(V0R)sinωt=I0sinωt For inductor L, voltage leads to current by π2 but both the currents IR and IL has same phase. ∴IL=V0XLsin(ωt)=I0sinωt ⇒IL=IR=I0sinωt Hence, option (D) is correct.

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