Alternating Current

Question 1

Steps to current in only resistive circuit derivation

Answer 1

V=vm sin (wt)
V=IR
I=vmsin(wt) /R
I=im sin(wt)

Question 2

Phase diff of current and voltage in only resistive

Answer 2

0.
They are in same phase

Question 3

Step of derivation of I for inductor circuit

Answer 3

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)

Question 4

Inductive reactance

Answer 4

Xl=wL

Question 5

Phase diff between V and I in inductive circuit

Answer 5

Current is pi/2 behind voltage

Question 6

Derivation of current for only capacitive circuit

Answer 6

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

Question 7

Capactive reactance

Answer 7

Xc=1/wC

Question 8

Phase diff between I and V in only capactive circuit

Answer 8

Current leads voltage by pi/2

Question 9

Impedence

Answer 9

Z=√R²+(Xc-Xl) ²

Question 10

Angle between Vr and V

Answer 10

Tan(phi)=vcm-vlm/vrm =(Xc-Xl) /R

Question 11

Explain impedence triangle

Answer 11

Hypo=Z
Theta= phi (between R and Z)
Adjacent=R
Opposite=Xc-Xl

Question 12

When is circuit predominantly inductive and capacitive

Answer 12

When Xc<Xl>Xl capacitive phi is positive</Xl>

Question 13

Current in series LCR

Answer 13

I’m=vm/Z

Question 14

At resonance Z

Answer 14

=R

Question 15

At resonance Xc and Xl

Answer 15

Xc=Xl

Question 16

Resonant frequency

Answer 16

w=1/√LC

Question 17

Power in LCR circuit the power factor

Answer 17

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)

Question 18

Power in only resistive circuit

Answer 18

Max
Phi=0
As cosphi=1

Question 19

Power in purely inductive or capacitive

Answer 19

0
Phi=pi/2

Question 20

Watless current

Answer 20

When current flows in circuit but no power is dissipated
Usually in purely inductive or capacitive circuit

Question 21

Power dissipated at resonance

Answer 21

Max

Question 22

Power factor

Answer 22

Cos phi

Question 23

Phi in LCR series

Answer 23

=tan(inverse) (Xc-Xl) /R

Question 24

Transformer

Answer 24

ip/is=vs/vp=Na/Np