(a) What is the maximum value of the current in the circuit? I max = A (b) What

Question

(a) What is the maximum value of the current in the circuit?
Imax = A

(b) What are the maximum values of the potential difference acrossthe resistor and the inductor?
VR,max = V
VL,max = V

(c) When the current is at a maximum, what are the magnitudes ofthe potential differences across the resistor, the inductor, andthe AC source?
VR = V
VL = V
Vsource = V

(d) When the current is zero, what are the magnitudes of thepotential difference across the resistor, the inductor, and the ACsource?
VR = V
VL = V
Vsource = V

Explanation / Answer

   we are given with
   f = 55 Hz    Vmax = 170 V    R = 1.2 k        = 1.2 x 103    L = 3.6 H    the inductive reactance is given by    XL = 2 f L          = ........    the impedence Z is given by    Z = [R2 + (XL -XC)2]    as XC = 0    Z = [R2 +(XL)2]        = ......... (a)    the maximum current will be    Imax = Vmax / Z            =........ A (b)    the maximum values of the potential differenceacross the resistor will be    VRmax = Imax R              = ........ V    the maximum values of the potential differenceacross the capacitor will be    VLmax = ImaxXL              = ........ V (c)    when the instantaneous current i is zero theinstantaneous voltage across the resistor is    vR = i R         = 0    the instantaneous voltage across the inductor isalways 90o or a quarter cycle out of phase with    the instantaneous current    so we get    when i = Imax    vL = 0    the kirchoffs rule always applies to theinstantaneous voltage around a closed loop    for the series circuit    vsource = vR +vL    when i = Imax    vsource = Imax R + 0               = ....... V (d)    when the instantaneous current is zero    the instantaneous voltage across the resistorwill be    vR = 0    the instantaneous voltage across theinductor is a quarter cycle out of phase with the current so    when i = 0 we must get    vL = VL,max         = ......... V    now applying the kirchoofs loop rule to theinstantaneous voltage around the series circuit at the    instant when i = Imaxgives    vsource = vR +vL                = 0 + VLmax                = ......... V         = ......... V    now applying the kirchoofs loop rule to theinstantaneous voltage around the series circuit at the    instant when i = Imaxgives    vsource = vR +vL                = 0 + VLmax                = ......... V

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