Find in an a.c. LCR circuit, a. resultant voltage b. impedance of the circuit c. phase difference d. average power
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Explanation:
From figure.
V
2
=V
R
2
+(V
C
−V
L
)
2
⟹V=
V
R
2
+(V
C
−V
L
)
2
...(i)
But, V
R
=Ri, V
C
=X
C
i, V
L
=X
L
i ...(ii)
where, X
C
=
ωC
1
=Capacitance reactance and X
L
=ωL=inductive reactance
V=
(Ri)
2
+(X
C
i−X
L
i)
2
Impedance of circuit, Z=
i
V
=
R
2
+(X
C
−X
L
)
2
i.e., Z=
i
V
=
R
2
+(X
C
−X
L
)
2
=
R
2
+(
ωC
1
−ωL)
2
Instantaneous current, I=
R
2
+(
ωC
1
−ωL)
2
V
0
sin(ωt+φ)
The phase difference (φ) between current and voltage V is given by tanφ=
R
X
C
−X
L
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