Question

5)A series circuit consisted of R= 4.7?, L= 2.0 mH , 2200 µF is connected to an alternative voltage with maximum voltage of V_m = 12.0 V and frequency of 60.0 Hz.

Find the following- show the formula- substitute- calculate – put final result in a box with its unit,

a ) Inductive Reactance

b)Capacitive Reactance

c) Impedance

d)maximum current in the circuit

e) Voltage across the resister

f)Voltage across the inductor.

g)Voltage across the capacitor

h) RMS voltage across the circuit V_rms?

I) Phase difference between the total current in the circuit and the voltage a across the circuit.

J) Resonance frequency of the circuit

k) Electric current in the circuit at resonance.

h) What happens at the resonance frequency?

show all the diagrams, formulas, substitutions, calculations, results, and unit for better understanding

Answer 1

a) inductive reactnce, XL = 2*pi*f*L

= 2*pi*60*2*10^-3

= 0.7540 ohms

b) Capacitive reactnace,

XC = 1/(2*pi*f*C)

= 1/(2*pi*60*2200*10^-6)

= 1.206 ohms

c) impedance, z = sqrt(R^2 + (XL - XC)^2)

= sqrt(4.7^2 + (0.7540 - 1.206)^2)

= 4.72 ohms

d) Imax = Vmax/z

= 12/4.72

= 2.54 A

e) VR = Imax*R

= 2.54*4.7

= 11.94 V

f) VL = Imax*XL

= 2.54*0.754

= 1.92 V

g) VC = Imax*XC

= 2.54*1.206

= 3.06 A

h) Vrms = Vmax/sqrt(2)

= 12/sqrt(2)

= 8.49 V

i) theta = tan^-1((XC - XL)/R)

= tan^-1( ( 1.206 - 0.754)/4.7)

= 5.50 degrees

j) resonant frequency, fo = 1/(2*pi*sqrt(L*C))

= 1/(2*pi*sqrt(2200*10^-6*2*10^-3))

= 75.9 Hz

k) I = Vmax/R

= 12/4.7

= 2.55 A

h) at resonant frequency, XL = XC

z = sqrt(R^2 + (XL - XL)^2)

z = R