Question

Explore The RLC series circuit llustrated in the Active Figure has R-1.94 ?, L -1.87 H, and C 198 ?F. The applied AC voltage has a frequency of f- 60 Hz and an rms voltage of AVmax 120 resistance inductance capacitance 1.0 1.0 1.0 1.0 1.0 1,5 1.5 2.0 2.0 ?? AUR UC (A) Find the inductive reactance, capacitive reactance, and impedance (B) Find the current through the circuit. (C) Find the phase difference between current and voltage (D) Find the voltages start reset Conceptualize There is a maximum voltage drop across each element given by the maximum current times the appropriate resistance, inductive reactance, or capacitive reactance for the corresponding element, and the maximum voltage drop across the three components equals the impedance times the maximum current. However, the instantaneous voltage across each element can oscillate with different phase from one element to another Display in a New Window

Answer 1

a)

Inductive Reactance

X_L=2pifL=2pi*60*1.87=704.62 ohms

Capacitive reactance

X_C=1/2pifC =1/2pi*60*(198*10^-6)=13.40 ohms

Impedance

Z=sqrt[R²+(X_L-X_C)²]=sqrt[1.94²+(704.62-13.40)²]

Z=691.22 ohms

b)

Current through the circuit

I=V/Z =120/691.22

I=0.17360 A

c)

phase difference

o=tan^-1(X_L-X_C/R)=tan^-1(704.62-13.40/1.94)

o=89.84^o

d)

V_R=0.1736*1.94=0.337 Volts

V_L=0.1736*704.62=122.32 Volts

V_C=0.1736*13.40=2.326 Volts