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A resistance and inductance are connecte...

A resistance and inductance are connected in series across a voltage,
`V=283sin314t`
The current is found to be `4sin(314t-pi//4)`. Find the value of the inductance and resistance.

Text Solution

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In L-R series cirucit current lags the voltage by an angle,
`phi = tan^(-1)(X_(L)/R)`
Here, `phi = pi/4`
`X_(L) = R` or `omegaL=R` `[omega=314 rad s^(-1)`
`therefore` 314 L = R ................(i)
Further, `V_(0) = I_(0)|Z|`
`therefore 283 = 4sqrt((R)^(2) + X_(L)^(2))`
or `R^(2) = (omegaL)^(2) = (283/4)^(2)=5005.56` (as `omegaL=R`
`therefore R=500 Omega`
and from Eqs (i), L=0.16 H
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