a resistor , an inductor and a capacitor are connected in series with a 120 V, 100Hz source. voltage leads the current by 35°in the circuit. if the resistance of the resistor is 10ohm and the sum of inductive and capacitive reactance is 17 ohm, calculate the self inductance of the inductor.
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Asked on December 26, 2019 by
Habeez Mhaske
A resistor, an inductor, and a capacitor are connected in series with a 120 V,100 Hz ac source. Voltage leads the current by 35
∘
in the circuit. If the resistance of the resistor is 10Ω and the sum of inductive and capacitive reactance is 17Ω, calculate self-inductance of the inductor.
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ANSWER
Given:-
phase difference ϕ=35°,R=10Ω
Sum of reactance of inductor and capacitor (X
L
+X
C
)=17⟶eq
n
(1)
Frequency of applied voltage, f=100Hz
So, angular frequency=2π×100
Now, for LCR circuit, we know
tanϕ=
R
X
L
−X
C
or X
L
−X
C
=Rtanϕ=10tan35°
X
L
+X
C
=17 [Using eq.1]
2X
L
=17+(10×0.7)
X
L
=12
ωL=12
L=
2π100
12
=1.9×10
−2
H
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