A series RLC circuit has R = 435 Ohm, L = 1.35 H, C = 3.2 muF. It is connected t

Question

A series RLC circuit has R = 435 Ohm, L = 1.35 H, C = 3.2 muF. It is connected to an AC source with/= 60.0 Hz and DeltaV_max = 150 V. Determine the inductive reactance, the capacitive reactance, and the impedance of the circuit. Conceptualize: The circuit of interest in this example is shown in the figure. The current in the combination of the resistor, inductor, and capacitor oscillates at a particular phase angle with respect to the applied voltage. A series circuit consisting of a resistor, an inductor, and a capacitor connected to an AC source. What if the frequency is now increased to f= 85 Hz, and we want to keep the impedance unchanged? (a) What new resistance should we use to achieve this goal? Follow the example closely. Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error, Ohm What is the phase angle (in degrees) between the current and the voltage now? Find the maximum voltages across each element.

Explanation / Answer

R = 435 ohm, L = 1.35 H, C = 3.2 uF, f = 60 Hz, V = 150 V

A) XL = wL = 2pi*f*L = 2pi*60*1.35 = 508.94 ohm

Xc = 1/wC = 1/(2pi*f*C) = 828.93 ohm

X = Xc - XL = 319.99 ohm

Z = sqrt[R^2 + X^2] = 540 ohm

B) a) XL = wL = 2pi*f*L = 2pi*85*1.35 = 721 ohm

Xc = 1/wC = 1/(2pi*f*C) = 585.13 ohm

X = XL - Xc = 135.87 ohm

Z = sqrt[R^2 + X^2] = 540 ohm

R^2 = 540^2 - 135.87^2

R = 522.63 ohm

b) Phase angle = arctan[X/R] = arctan(135.87/522.63) = 14.57 degree

c) VR = 150 V

VC = Xc*Vo/sqrt[R^2 + Xc^2] = 585.13*150/784.55 = 111.87 V

VL = XL*Vo/sqrt[R^2 + XL^2] = 721*150/890.5 = 121.5 V

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