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AC voltage applied to an inductor is considered one the most difficult concept.
43 Questions around this concept.
A sinusoidal voltage V(t) = 100 sin (500t) is applied across a pure inductance of L = 0.02 H. The current through the coil is :
Phase difference b/w voltage & current in the inductive circuit is
Calculate the power in given circuit
The plot of inductive reactance & frequency of source is
A sinusoidal voltage of 50sin (300t) is applied across a pure inductor of L = 0.01H. The current through the coil is :
The correct statement about pure inductive circuit is-
Calculate the Reactance in given circuit
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Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): A choke coil is simply a coil having a large inductance but a small resistance. Choke coils are used with fluorescent mercury-tube fittings. If household electric power is directly connected to a mercury tube, the tube will be damaged.
Reason (R): By using the choke coil, the voltage across the tube is reduced by a factor of $\left(R / \sqrt{R^2+\omega^2L^2}\right)$, where $\omega$ is the frequency of the supply across resistor R and inductor L. If the choke coil were not used, the voltage across the resistor would be the same as the applied voltage.
In light of the above statements, choose the most appropriate answer from the options given below:
AC voltage applied to an inductor
Voltage applied in the circuit is V=V0sinωt is applied to pure inductor coil of inductance L. As the current through the inductor varies and opposing induced emf is generated in it and is given by $-L \frac{d i}{d t}$
From Kirchhoff's loop rule:
$
V_0 \sin \omega t-L \frac{d i}{d t}=0
$
or
$
d i=\frac{V_0}{L} \sin \omega t d t
$
Integrating both sides we get,
$
i=-\frac{V_0}{\omega L} \cos \omega t+C
$
Where C is the constant of integration. This integration constant has dimensions of current and is independent of time. Since source has an emf which oscillates symmetrically about zero, the current it sustain also oscillates symmetrically about zero, so there is no time independent component of current that exists. Thus constant $\mathrm{C}=0$.
So we have,
$
\begin{aligned}
i & =\frac{-V_0}{\omega L} \cos \omega t \\
& =\frac{V_0}{\omega L} \sin \left(\omega t-\frac{\pi}{2}\right) \\
i & =i_0 \sin \left(\omega t-\frac{\pi}{2}\right)
\end{aligned}
$
Where $i_0=\frac{V_0}{\omega L}$ is called peak value of the current.
From instantaneous values of current and voltage we see that in pure inductive circuit the current lags behind emf by a phase angle of π/2.
This phase relationship is graphically shown below in the figure-
Since peak value of current in the coil is $\qquad$
Comparing it with the ohm's law we find product $\omega \mathrm{L}$ has dimension of resistance and it can be represented by
$
X_L=\omega L
$
where $X_L$ is known as reactance of the coil which represents the effective opposition of the coil to the flow of alternating current.
Phase difference (between voltage and current):
$
\phi=+\frac{\pi}{2}
$
Power factor:
$
\cos (\phi)=0
$
Time difference:
$
\mathrm{T} . \mathrm{D}=\frac{T}{4}
$
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