Question

Constants You have a resistor of resistance 190 Ω , an inductor of inductance 0.410 H , a capacitor of capacitance 5.50 μF and a voltage source that has a voltage amplitude of 28.0 V and an angular frequency of 270 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 D: Does the source voltage lag or lead 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?

Answer 1

capacitive reactance, X_c = 1/(wC) = 1/(270*5.5*10^-6) = 673.4 ohm

inductive reactance, X_L = wL = 270*0.41 = 110.7 ohm

A) impedence is given by, Z=sqrt(R² + (X_c - X_L)²) = sqrt(190²+(673.4-110.7)²) = 593.911 ohm

B) current,i = V/Z = 28/593.11 = 0.0472 Amp

C) phase angle, $\phi$ = tan^-1((X_L-X_c)/R) = tan^-1((110.7-673.4)/190)

$\phi$ = -71.342^o

D) Source voltage lags

E) V_R = i*R = 0.0472*190 = 8.968 V

F) V_C = i*X_c = 0.0472*673.4 = 31.784 V

G) V_L = i*X_L = 0.0472*110.7 = 5.225 V