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otester
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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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