b) What is the current through the 100 ohm resistor? c) What is the voltage drop

Question

b) What is the current through the 100 ohm resistor? c) What is the voltage drop across one of the 200 ohm resistor? d) What is the power dissipated by the circuit? A separate RLC series circuit has a source supplying rms voltage of 12 V at a frequency of 60 Hz, The circuit contains a resistor of 200 ohm, an inductor of 100 mH, and a capacitor of 200 mu F. e) What is the inductive reactance of the circuit? f) What is the capacitive reactance of the circuit? g) What is the impedance of the circuit? h) What is the rms current in the circuit? i) What is the phase angle, phi, of the source voltage to current? j) What is the power dissipated by the circuit? What is the impedance of the circuit when it is at resonance?

Explanation / Answer

(A) two 200 ohm are in parallel,

1/R = 1/200 + 1/200 = 2 / 200

R = 100 ohm

now R and 100 ohm are in series.

Req = 100 + 100 = 200 ohm

(B) battery and 100 ohm are in series so same current throug them,

I = V / Req =12 / 200 = 0.06 A

(C) V = 12 - (0.06 x 100) = 6 volt

(d) P = V I = 0.06 x 12 = 0.72 W

(e)XL = 2 pi f L = 2 x pi x 60 x 0.100 = 37.7 ohm

(f) Xc = 1 / (2 pi f C) =1 / (2 xpi x 60 x 200 x 10^-6)

Xc = 13.3 ohm

(g) Z = sqrt[ R^2 + (XL - Xc)^2]

R = 200 ohm

Z = 201.5 ohm

(h) Irms = Vrms / Z = 12 / 201.5 = 59.6 mA

(I) phi = tan^=1[ 37.7 - 13.3 ) / 200 ] = 7 deg

(j) P = Irms^2 R = 0.0596^2 x 200 = 0.71 W

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