An AC power source with Vm = 220 V and f = 60.0 Hz is connected in a series RLC

Question

An AC power source with Vm = 220 V and f = 60.0 Hz is connected in a series RLC circuit. The resistance, R, inductance, L, and capacitance, C, of this circuit are, respectively, 47.0 O, 0.240 H, and 0.045 mF. Find each of the following quantities. (When entering units, use ohm for O.)

(a) the inductive reactance

(b) the capacitive reactance

(c) the impedance of the circuit

(d) the maximum current through the circuit (based on the frequency given above)

(e) the maximum potential difference across each circuit element

Explanation / Answer

  Here   Vm = 220 V and f = 60.0 Hz = 376.99 rad/sec

   R= 47.0 Ohm, L = 0.240 H, and C = 0.045 mF

   a) inductive reactance XL = L = 90.48 Ohm.

  b)capacitive reactance XC = 1/ C = 58.95 kOhm

c) impedance of the circuit Z = R + j (XL - XC ) =0.0 47 - j 58.85 k Ohm

d) I(max) = V(max) / Z = 3.74 mA.

e) maximum potential difference across resistor is

   V = R * I(max) = 0.176 V

   maximum potential difference across inductor is

   V = XL* I(max) = 0.338 V

   maximum potential difference across resistor is

   V = XC * I(max) = 220.473 V

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