Abswer all parts In a simple AC circuit shown on the right, C = 0.0015 F, L = 1.
ID: 1497606 • Letter: A
Question
Abswer all parts
In a simple AC circuit shown on the right, C = 0.0015 F, L = 1.7 H, R = 75 ohm, and delta V = delta V_max sin(omega t), where delta V_max = 5.5 V and omega = 42 rad/s. Randomized variables C = 0.0015 F L = 1.7 H R = 75 ohm delta V_max = 5.5 V omega = 42 rad/s Express the capacitive reactance, X_c, in terms of C, and omega. Calculate the numerical value of X_c in ohms. Express the inductive reactance, X_L, in terms of L, and omega. Calculate the numerical value of X_L in ohms. Express the impedance, Z, in terms of R,X_L, and X_c. Calculate the numerical value of Z in ohms. Express the maximum current I_max, in terms of delta V_max and Z. Calculate the numerical value of I_max in A. Express the tangent of the phase angle between current and source voltage, phi, in terms of X_L, X_c, and R. Calculate the numerical value of phi in radians.Explanation / Answer
(a) Xc = 1/(wC)
(b) Xc = 1/(42 x 0.0015) = 15.873 ohm
(c) XL = wL
(d) XL = 42 x 1.7 = 71.4 ohm
(e) Z = sqrt(R2 +(XL-XC)2)
(f) Z = sqrt(752 + (71.4 - 15.873)2) = 93.32 ohm
(g) Imax = Vmax/Z
(h) Imax = 5.5/93.32 = 0.05894 A
(i) tan(phi) = (XL-XC)/R
(j) phi = tan-1(71.4-15.873)/75 = 36.515o = 0.6373 radian