(a) What is the maximum value of the current in the circuit? Imax = (b) What are
ID: 1697420 • Letter: #
Question
(a) What is the maximum value of the current in the circuit?Imax =
(b) What are the maximum values of the potential difference across the resistor and the inductor?
?VR,max =
?VL,max =
(c) When the current is at a maximum, what are the magnitudes of the potential differences across the resistor, the inductor, and the AC source?
?VR =
?VL =
?Vsource =
(d) When the current is zero, what are the magnitudes of the potential difference across the resistor, the inductor, and the AC source?
?VR =
?VL =
?Vsource =
Explanation / Answer
frequency f = 56 Hz maximum voltage V_max = 170 V resistance R = 1.2 kO = 1.2 x 10^3 O inductance L = 2.4 H the inductive reactance is given by X_L = 2 p f L substitute the given data in above equation we get X_L value. the impedence Z = v[R^2 + (X_L -X_C)^2] , (since X_C = 0) Z = v[R^2 +(X_L)^2] substitute the given data in above equation we get 'Z' value. ........................................................................................ (a) the maximum value of the current in the circuit is I_max = V_max / Z substitute the X_L and Z values in above equation we get 'I_max' value I_max=........ A ........................................................................................... (b) the maximum values of the potential difference across the resistor is VR,max = (I_max)(R) substitute the 'I_max' and 'R' values in above equation we get 'VR,max' value VR,max = ........ V the maximum values of the potential difference acrossthe capacitor will be VL,max = (I_max)(X_L) VL,max = ........ V ................................................................................................... (c) when the instantaneous current i is zero the instantaneous voltage across the resistor is v_R = i R = 0 the instantaneous voltage across the inductor is always 90 deg or a quarter cycle out of phase with the instantaneous current so we get, when i = I_max and ?vL = 0. apply kirchoffs rule , v_source = v_R + v_L when i = Imax v_source = (I_max) (R) + 0 v_source = ....... V ........................................................................................... (d) when the instantaneous current is zero the instantaneous voltage across the resistor v_R = 0 the instantaneous voltage across the inductor is a quarter cycle out of phase with the current so when i = 0 we must get v_L = ?VL,max v_L = ......... V now applying the kirchoff laws when i = I_max v_source = v_R + v_L = 0 + VL,max v_source = ......... V
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