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In an LR-circuit, the inductive reactanc...

In an `LR`-circuit, the inductive reactance is equal to the resistance `R` of the circuit. An e.m.f `E=E_(0)cos (omegat)` applied to the circuit. The power consumed in the circuit is

A

`(E_(0)^(2))/(R)`

B

`(E_(0)^(2))/(2R)`

C

`(E_(0)^(2))/(4R)`

D

`(E_(0)^(2))/(8R)`

Text Solution

Verified by Experts

The correct Answer is:
C
`P=E_("rms")i_("rms")cos varphi=(E_(0))/(sqrt(2))xx(i_(0))/(sqrt(2))xxR/Z`
`implies (E_(0))/(sqrt(2))xx(E_(0))/(Zsqrt(2))xxR/Z implies P=(E_(0)^(2)R)/(2Z^(2))`
Given `X_(L)=R`, so `Z=sqrt(2)R implies P=(E_(0)^(2))/(4R)`
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