Question

When an inductor is connected to a 230 V dc source, a current of 2 A passes through it. When
the same inductor is connected to a 230 V, 50 Hz ac source, the amount of current decreases. why​

Answer 1

Answer:

Here is your answer..

In the problem we are given that :

DC voltage V dc :100DC.

DC current through the solenoid I dc :1A.

Therefore, according to Ohms’s law:

We know that:

V dc = I dc R

R=V dc /I dc

R=100/1=100Ω

We are also given that:

The AC voltage V ac =100AC.

The AC current I ac =0.5AC.

Frequency (v)of AC source =50Hz.

From the formula of an RLC circuit ,

We know that:

Z=V 0 /i 0 =√[R 2 +(X L – X C ) 2 ]

Since in this numerical we do not have capacitance ,X C =0.

The formula therefore becomes:

Z=√(R 2 +X L 2 )

Where,

Z=impedence (i.e the total effective resistance of the RL circuit)

R=resistance of DC source.

X L =Inductive reactance.

R here is 100Ω. (as calculated from above)

Z=V AC /I AC

=100/0.5=200Ω……………………………………….(I AC = 0.5A given)

We know that:

X L= ω L

=2πvL…………………………………….

.(where ω = 2πv , and v is the frequency which is given as 50 Hz)

= 2*3.14*50*L

=314L

X L 2 = 314 2 *L 2 = 98596L 2

R 2 = 100 2 = 10000Ω…………………..( value of R is calculated above as 100Ω)

Z 2 = 40000Ω

Putting the value of Z, R 2 ,X L 2 in the equation of the R-L circuit we get,

200 = √ (10000+98596L 2 )

Squaring both sides we get,

40000 = 10000 + 98596 L 2

30000 = 98596L 2

L = 0.55H

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Answer 2

The amount of ac current decreases.

Explanation:

Given that,

Voltage of dc source = 230 V

Current = 2 A

Frequency = 50 Hz

When dc source used then an inductor acts resistor.

We need to calculate the resistance

Using ohm's law

$R=\dfrac{V}{I}$

Put the value into the formula

$R=\dfrac{230}{2}$

$R=115\ \Omega$

The ac current is

$I_{ac}=\dfrac{V}{R}$

When ac source used then both R and $\Delta L$ are coincident together which is become impedance.

$z=\sqrt{R^2+X_{L}^2}$

We know that,

$X_{L}=2\pi fL$

So, $z>R$

The ac current is

$I_{ac}=\dfrac{V}{z}$

So, $I_{dc}>I_{ac}$

Hence, The amount of ac current decreases.

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Topic  : impedance

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