In a simple AC circuit shown on the right, C = 0.0055 F, L = 1.9 H, R = 55 ohm a
ID: 1610139 • Letter: I
Question
In a simple AC circuit shown on the right, C = 0.0055 F, L = 1.9 H, R = 55 ohm and delta V = delta V_max sin(omega t), where delta V_max = 2.5 V and omega = 49 rad/s. Express the capacitive reactance, X_C, in terms of C, and omega. X_C = 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/wc = 1/49*0.0055 = 3.71 ohm
c) xl = wl
d) xl = 49*1.9 = 93.1 ohm
e) z = sqrt(r^2+(xl-xc)^2)
f) z = sqrt(55^2+89.39^2) = 104.96 ohm
g) i max = v,max/z
h) i max = 2.5/104.96 = 0.0238 A