A coil and an inductance `-` free resistance `R=25 Omega` are connected in parallel to the `ac1` mains. Find the heat power generated in the coil provided a current `I=0.90 A` is drawn from the mains. The coil and the resistance `R` carry currents `I_(1)=0.50 A` and `I_(2)=0.60 A` respectively.

Explanation

Voltage across resistance `V = 0.6 xx 25 =15V`
Current in the coil lags the voltage by `phi` current in `25Omega` is in same phase with voltage
`(0.9)^(2) = (0.6)^(2) + (0.5)^(2) + 2 xx 0.6 xx 0.5 cos phi`
`0.81 = 0.36 + 0.25 + 0.6 cos phi`
`cos phi = (1)/(3)`
power consumed in coil is
`V i cos phi = 15 xx 0.5 xx (1)/(3) =2.5 W`

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