Question

A sinusoidal voltage Av = 37.5 sin(100t), where Av is in volts and t is in seconds, is applied to a series RLC circuit with L = 170 mH, C = 99.0 pF, and R = 54.0 N. (a) What is the impedance (in ) of the circuit? 22 (b) What is the maximum current in A)? A (c) Determine the numerical value for w in rad/s) in the equation i = Imax sin(wt - 0). rad/s (d) Determine the numerical value for q (in rad) in the equation i = Imax sin(wt - 4). rad (e) What If? For what value of the inductance in H) in the circuit would the current lag the voltage by the same angle was that found in part (d)? H (f) What would be the maximum current (in A) in the circuit in this case? A

Answer 1

Given,

delV = 37.5 sin(100 t) ; L = 170 mH ; C = 99 uF ; R = 54 Ohm

a)We know that

Z = sqrt[R^2 + (Xl - Xc)^2]

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

Z = sqrt[54^2 + (100 x 0.170 - 1/100 x (99 x 10^-6))^2] = 99.87 Ohm

Hence, Z = 99.87 Ohm

b)I(max) = Vmax/Z

I(max) = 37.5/99.8 = 0.376 A

Hence, I(max) = 0.376 A

c)w = 100 rad/s

d)phi = pi/2

phi = 3.14/2 = 1.57 rad/s

Hence, phi = 1.57 rad/s