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28 Common Questions of a Simple Alternating Current Circuit

physics.fisikastudycenter.com,- Learning ac current circuit in 28 common questions of a single ac current circuit problem. This topic discussed at grade 12 high school.


Problem

Given an ac circuit contents a resistor (R), an inductor (L) and a capacitor (C) in series combination with voltage source of V = 120 sin (125t) volt.


Questions

  • a) angular frequency of the ac source
  • b) frequency of the ac source
  • c) period of ac source
  • d) voltage amplitude of ac source
  • e) effective voltage of ac source
  • f) peak to peak voltage of ac source
  • g) inductive reactance of the inductor
  • h) capacitive reactance of the capacitor
  • i) circuit impedance
  • j) amplitude of circuit current
  • k) root-mean-square current of circuit
  • l) voltage across d-e
  • m) voltageacross e-f
  • n) voltage across f-g
  • o) voltage across d-f
  • p) voltage across e-g
  • q) voltage across d-g
  • r) circuit power factor
  • s) phase angle
  • t) power dissipated in the circuit
  • u) Circuit properties whether resistive, inductive or capacitive
  • v) instantaneous value of voltage when t = (π/150) sec
  • w) current equation of ac source
  • x) instantaneous value of current of ac source when t = (0,016 π)
  • y) average voltage
  • z) current average
  • aa) current and voltage in phasor
  • bb) resistance, inductive reactance and capacitive reactance in phasor

Answers
a) Expression of sinusoidal voltage



where V is the instataneous value at time t, Vmax is the amplitude (maximum value), ω is the angular frequency. So then ω = 125 rad/s


b) angular frequency calculation :



c) period :



d) amplitude of voltage:



e) efective voltage or root-mean-square voltage :



f) peak to peak voltage :



g) inductive reactance :



h) capacitive reactance :



i) circuit impedance :



j) amplitude of current (maximum value) :



k) root-man-square current:



l) voltage across d-e :

We assume the voltage as the efective value, and the current is effective value Ief



m) voltage across e-f :



n) voltage across f-g:

o) voltage across d-f :



where VR , VL and VC are the voltage acorss R, the voltage across L and the voltage across C respectively.

There is no capacitor on d-f, so then the equation above becomes:

p) voltage across e-g :

q) voltage across d-g:

r) power factor (pf) :
pf = cos φ = R/Z = 8/10 = 0.8

or use anaother relationship

pf = cos φ = VR/V

s) angle phase between I and V ::



t) power dissipated in the circuit :



u) Circuit properties whether resistive, inductive or capacitive

To define the properties of circuit if :

XL > XC → inductive circuit

XC > XL capacitive circuit

XL = XC resistive circuit

So then the circuit is capacitive

v) instantaneous value of V at t = ( π/150) sec:



w) current equation of ac source :

For V = Vmax sin ω t
the current equation is:

I = Imax sin (ωt + φ) → capacitive circuit
I = Imax sin (ωt − φ) → inductive circuit
The circuit is capacitive so then use he first equation

x) instantaneous value of current at t = (0,016 π) sec :



y) average voltage :



z) average current :



aa) phasor diagram

 

 

bb) phasor diagram of R, XL and XC

 

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