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Was wondering if anyone can confirm that I am on the right track or not?

I'm not sure whether Irms is meant to be a complex number not :/

Thanks in advance,

otester

A complex voltage v(t)=60sin(3wt)+15sin(3wt)+10sin(5wt) volts is applied to a coil of inductance 5mH and resistance 6(ohms). Determine, for a fudamental frequency of 100Hz, (a) an expression to represent the instantaneous value of current, (b) the rms voltage, (c) the rms current, (d) the power dissipated.

XL = 2(pie)fL

Impedance (Z) = R + jXL

RMS current (Irms) = Vrms/Z

w = (omega)

Power dissipated=(Irms)x(Vrms)

(a) XL = 2(pie)100x(5x10^-3) = 31.42(ohms)

Z = 6+j31.42

Irms = ( 60sin(3wt)+15sin(3wt)+10sin(5wt) ) / ( 6+j31.42 )

(b) Vrms = sqrt( (60^2+15^2+10^2)/2 ) = 44.3x0.707 = 31.32V

(c) Irms = 31.32 / ( 6+j31.42 ) = 5.22+j0.997

(In polar form: 5.31 @ 10.81 (degrees))

(d) Power dissipated = (31.32)x(5.31 @ 10.81) = 36.63 @ 10.81

I'm not sure whether Irms is meant to be a complex number not :/

Thanks in advance,

otester

## Homework Statement

A complex voltage v(t)=60sin(3wt)+15sin(3wt)+10sin(5wt) volts is applied to a coil of inductance 5mH and resistance 6(ohms). Determine, for a fudamental frequency of 100Hz, (a) an expression to represent the instantaneous value of current, (b) the rms voltage, (c) the rms current, (d) the power dissipated.

## Homework Equations

XL = 2(pie)fL

Impedance (Z) = R + jXL

RMS current (Irms) = Vrms/Z

w = (omega)

Power dissipated=(Irms)x(Vrms)

## The Attempt at a Solution

(a) XL = 2(pie)100x(5x10^-3) = 31.42(ohms)

Z = 6+j31.42

Irms = ( 60sin(3wt)+15sin(3wt)+10sin(5wt) ) / ( 6+j31.42 )

(b) Vrms = sqrt( (60^2+15^2+10^2)/2 ) = 44.3x0.707 = 31.32V

(c) Irms = 31.32 / ( 6+j31.42 ) = 5.22+j0.997

(In polar form: 5.31 @ 10.81 (degrees))

(d) Power dissipated = (31.32)x(5.31 @ 10.81) = 36.63 @ 10.81

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