I JUST NEED D A sinusoidal voltage ? v = 41.0 sin 100 t , where ? v is in volts

Question

I JUST NEED D

A sinusoidal voltage ?v = 41.0 sin 100t, where ?v is in volts and t is in seconds, is applied to a series RLC circuit with L = 180 mH, C = 99.0

A sinusoidal voltage ?v = 41.0 sin 100t, where ?v is in volts and t is in seconds, is applied to a series RLC circuit with L = 180 mH, C = 99.0 µF, and R = 53.0 ?. What is the impedance of the circuit? What is the maximum current? Determine the numerical value for ? in the equation i = Imax sin (?t ? phi ). Determine the numerical value for phi in the equation i = Imax sin (?t ? phi ). Does the current lead or lag the voltage in this circuit? rad

Explanation / Answer

R=53

XL=wL=100*0.18=18ohms

XC=1/(wC)=101.01 ohms

So

|Z|=sqrt(R^2+(XL-XC)^2)=98.487 ohms

max current=41/Z=0.4163A

Z=53-83.01j

So

I=41angle(0)/Z=0.4163angle(57.443)=0.4163sin(100t+57.443deg)=0.4163sin(100t+1rad)

So

w=100rad/s

and

phi=-1 rad

current leads

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