An ideal inductor takes a current of `10` A when connected to a `125V` 50Hz ac supply A if the two are connected in series across a `100sqrt2` V ,40 Hz supply the current throught the circuit will be .

Options

A. `10A`
B. `12.5A`
C. `20A`
D. `25A`

Answer

A

Explanation

`i_(1) = 10A X_(L) = 2pi fL =100 piL`
`i_(1) = (V)/(X_(L)) implies 10 = (125)/(100piL)`
` 100 piL = 12.5 implies piL = (12.5)/(100)`
`i_(2) =12.5 A, i_(2) = (V)/R implies 12.5 = (125)/( R)`
`R =10 Omega`
`X_(L) = 2pi f L =2pi xx 40 L = 80 piL = 80 xx (12.5)/(100)`
`10 Omega`
`Z = sqrt(R^(2) + X_(L)^(2)) =sqrt((10)^(2) + (10)^(2) ) = 10sqrt2 Omega`
`i = (V)/(Z) = (100sqrt2)/(10sqrt2) = 10A`


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