PLEASE describe solution clearly in words. Thanks! Consider a series RLC circuit

Question

PLEASE describe solution clearly in words. Thanks!

Consider a series RLC circuit with R = 100 Ohm, L = 75 mH and C = 1.0 muF. Suppose it is driven by an AC voltage source with V0 = 2.0 V at a frequency of 1.0 kHz. What is the maximum current flowing in the circuit? What is the maximum voltage across the resistor, capacitor and inductor in the circuit? What is the phase angle between the total voltage and the current? What average power is dissipated in the circuit? What is the resonant frequency of the circuit in Hertz?

Explanation / Answer

capacitive reactance = -j/wc = -j159.15 ;w=2x1000

inductive reactance = j wL = j 471.23

voltage v = Vosinwt = 2sinwt 20deg V

Zeq = 100 + j(471.23-159.15) =100+ j312

current = 20 / (100+j312) = 6.1 -72.2deg mA

a)hence the max current flowing = 6.1 x 10 ^-3 A = 6.1 mA

b) max voltage across

resistor = 100x6.1 mA = .61 V

capacitor= 159.15 x 6.1mA = .97V

inductor = 471.23 x 6.1mA = 2.874 V

c) phase angle = -72.2 deg

d) avg power dissipated = V I cos( phase angle) = 2x 6.1x 10^-3 x cos 72.2 = 3.73 x 10^-3 = 3.73 mW

e) resonant frequency = 1/2LC = 581.15 Hz

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