Aseries rlc circuit (l = 24 mh, c = 40 μf, and r = unknown) has an ac generator with frequency f = 310 hz and amplitude emax = 120 v. the peak instantaneous current in the circuit is imax = 1.4 a. what is φ = the phase angle between the driving emf and the current in the circuit? define φ to be positive if the voltage leads the current and φ to be negative if the current leads the voltage. φ =

φ = +23.32  (voltage leads the current)

φ = -23.32  (current leads the voltage)

Explanation:

XL = 2πfL = 2π(310)(24 ×10^-3) = 46.77 Ω

Xc = 1/2πfC = 1/2π(310)(40) =  12.85 Ω

If we draw the impedance triangle, then XL and Xc are on opposite axis. So,

XL – Xc = 46.77 – 12.85 = 33.93 Ω

Now,

Impedance = Z = Emax/Imax = 120/1.4 = 85.71 Ω

If we consider impedence triangle then,

Sin φ = (XL – Xc)/Z

φ =Arc sin (XL – Xc)/Z = Arc sin (33.93/85.71) = + 23.32

If current leads the voltage, then the sign of the phase angle will be reversed. So,

φ = -23.32