A sinusoidal voltage Delta v = 41.0 sin 100 t, where Delta v is in volts and t i

Question

A sinusoidal voltage Delta v = 41.0 sin 100 t, where Delta v is in volts and t is in seconds, is applied to a series RLC circuit with L = 190 mH, C = 99.0 mu F, and R = 71.0 ohm. (a) What is the impedance of the circuit? Is the 100 in the equation Delta V/(t) = (41.0 V) sin(100t) equal to the frequency or the angular frequency? ohm (b) What is the maximum current? You appear to be calculating this correctly using your incorrect result for the impedance. A (c) Determine the numerical value for omega in the equation i = I_max sin (omega t - phi). rad/s (d) Determine the numerical value for phi in the equation i = I_max sin (omega t - phi). What quantities are need to calculate the phase angle? rad

Explanation / Answer

a] impedence Z = sqrt(R^2+ (wL - 1/wC)^2)

= sqrt(71^2 + (100*0.190 - 1/(100*99e-6))^2)

= 108.47 ohm

b] imax = Vmax/Z = 41/108.47 = 0.378 A

d] phi = arccos (71/108.47) = 0.857 rad

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