Alternating Current Flashcards
Steps to current in only resistive circuit derivation
V=vm sin (wt)
V=IR
I=vmsin(wt) /R
I=im sin(wt)
Phase diff of current and voltage in only resistive
0.
They are in same phase
Step of derivation of I for inductor circuit
V=vm sin(wt)
By KVL v-Ldi/dt=0
di/dt= V/L
I=vm/wL sin(wt-pi/2)
im=vm/wl=vm/Xl
I=im sin(wt-pi/2)
Inductive reactance
Xl=wL
Phase diff between V and I in inductive circuit
Current is pi/2 behind voltage
Derivation of current for only capacitive circuit
V=vm sin(wt)
V=Q/C
vm sin(wt) =Q/C
Q=vmC sin(wt)
I=dq/dt
I=d/dt(vmCsin(wt))
I=im sin(wt+pi/2)
im=vmwC=vm/Xc
Capactive reactance
Xc=1/wC
Phase diff between I and V in only capactive circuit
Current leads voltage by pi/2
Impedence
Z=√R²+(Xc-Xl) ²
Angle between Vr and V
Tan(phi)=vcm-vlm/vrm =(Xc-Xl) /R
Explain impedence triangle
Hypo=Z
Theta= phi (between R and Z)
Adjacent=R
Opposite=Xc-Xl
When is circuit predominantly inductive and capacitive
When Xc<Xl>Xl capacitive phi is positive</Xl>
Current in series LCR
I’m=vm/Z
At resonance Z
=R
At resonance Xc and Xl
Xc=Xl
Resonant frequency
w=1/√LC
Power in LCR circuit the power factor
p=vi=vmsin(wt) im sin(wt+phi)
By 2ss=c-c
P=vmim/2 (cos(phi)-cos(2wt+phi))
As 2nd term of eq depends on t it’s avg is 0
P=vmim/2cosphi
P=VIcos(phi)
P=I²Z cos(phi)
Power in only resistive circuit
Max
Phi=0
As cosphi=1
Power in purely inductive or capacitive
0
Phi=pi/2
Watless current
When current flows in circuit but no power is dissipated
Usually in purely inductive or capacitive circuit
Power dissipated at resonance
Max
Power factor
Cos phi
Phi in LCR series
=tan(inverse) (Xc-Xl) /R
Transformer
ip/is=vs/vp=Na/Np
