You have a resistor of resistance 200 , an inductor of inductance 0.410 H , a ca

Question

You have a resistor of resistance 200 , an inductor of inductance 0.410 H , a capacitor of capacitance 5.80 F and a voltage source that has a voltage amplitude of 26.0 V and an angular frequency of 300 rad/s . The resistor, inductor, capacitor, and voltage source are connected to form an L-R-C series circuit.

Part A

What is the impedance of the circuit?

Part B

What is the current amplitude?

Part C

What is the phase angle of the source voltage with respect to the current?

Part E

What is the voltage amplitude across the resistor?

Part F

What is the voltage amplitude across the inductor?

Part G

What is the voltage amplitudes across the capacitor?

Explanation / Answer

Impendece in RLC circuit is given by Z^2 = R^2+(XL-XC)^2

where XL = inductivereactance = WL = 2pifL = 300 * 0.410 = 123 ohms

Xc = capcacitve reactnace = 1/WC = 1/(2pifC) = 1/(300 *5.8*10^-6)

Xc = 574.7 ohms

so Z^2 = 200^2 + (574.7 - 123)^2

Z = 494 ohms

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now current I = V/Z = 26/494 = 0.0526 Amps

-----------------------------

phase angle tan theta = (XL-Xc)/R = (123 - 494)/200

theta = -61.67 deg

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Volatge across resistor VR = iR = 0.0526 * 200 = 10.52 Volts

Volatge across inductor VL = iXL = 0.0526 * 123 = 6.46 Volts

Voltage across capacitor Vc = iXC = 0.0526 * 494 = 26 Volts

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