Answer
439.2k+ views
Hint: Inductive reactance is directly proportional to frequency of AC source. As frequency increases inductive reactance also increases.
Formula used:
Impedance of the coil,$Z = \sqrt {\left( {{R^2} + {X^2}_L} \right)} $
Where, r is the resistance of the coil (ohm), ${X_L}$ is the inductive reactance (ohm)
Current in the coil,$I = \dfrac{{{V_{rms}}}}{Z}$
${V_{rms}}$ Is the RMS value of voltage (V)
Complete step by step answer:
Given, resistance of the coil r=30ohm
The inductive reactance of the coil ${X_L}$=20 ohm
Frequency, f=50hz, ${V_{rms}}$=200v
We know that ${X_L} = \omega L$
$ = 2\pi fL$
Then,$20 = \left( {2\pi } \right)50 \times L$ ……………………. (1)
When frequency of ac source is changed to 100hz, then
${X^I}_L = {\omega ^I}L$
$ = 2\pi {f^I}L$
Then,${X^I}_L = \left( {2\pi } \right)100L$
Above equation can be rearranged as,
${X^I}_L = \left( {2\pi } \right)50 \times L \times 2$
Now substitute equation (1) in the above equation we get,
${X^I}_L = 20 \times 2 = 40\Omega $
Therefore,
Impedance of the coil,$Z = \sqrt {\left( {{R^2} + {X^I}{{^2}_L}} \right)} $
$Z = \sqrt {\left( {{{30}^2} + {{40}^2}} \right)} = 50\Omega $
Then, current in the coil,$I = \dfrac{{{V_{rms}}}}{Z}$
$I = \dfrac{{200}}{{50}}$
$ = 4A$
So, the correct answer is “Option B”.
Additional Information:
When l or c is present in an ac circuit, energy is required to build up the magnetic field around l or electric field in c. This energy comes from the source. However, power consumed in l or c is zero because all the power received from the source in a quarter cycle is returned to the source in the next quarter cycle. This power oscillates back and forth and is called reactive power. The total opposition to alternating current in an AC circuit is called impedance of the circuit Z.
Note:
1. Opposition offered by an inductor for the flow of ac is called ‘inductive reactance’.
2. An alternating voltage is one whose magnitude changes with time and direction changes periodically.
3. Frequency of direct current is zero. That is direct current is independent of frequency.
Formula used:
Impedance of the coil,$Z = \sqrt {\left( {{R^2} + {X^2}_L} \right)} $
Where, r is the resistance of the coil (ohm), ${X_L}$ is the inductive reactance (ohm)
Current in the coil,$I = \dfrac{{{V_{rms}}}}{Z}$
${V_{rms}}$ Is the RMS value of voltage (V)
Complete step by step answer:
Given, resistance of the coil r=30ohm
The inductive reactance of the coil ${X_L}$=20 ohm
Frequency, f=50hz, ${V_{rms}}$=200v
We know that ${X_L} = \omega L$
$ = 2\pi fL$
Then,$20 = \left( {2\pi } \right)50 \times L$ ……………………. (1)
When frequency of ac source is changed to 100hz, then
${X^I}_L = {\omega ^I}L$
$ = 2\pi {f^I}L$
Then,${X^I}_L = \left( {2\pi } \right)100L$
Above equation can be rearranged as,
${X^I}_L = \left( {2\pi } \right)50 \times L \times 2$
Now substitute equation (1) in the above equation we get,
${X^I}_L = 20 \times 2 = 40\Omega $
Therefore,
Impedance of the coil,$Z = \sqrt {\left( {{R^2} + {X^I}{{^2}_L}} \right)} $
$Z = \sqrt {\left( {{{30}^2} + {{40}^2}} \right)} = 50\Omega $
Then, current in the coil,$I = \dfrac{{{V_{rms}}}}{Z}$
$I = \dfrac{{200}}{{50}}$
$ = 4A$
So, the correct answer is “Option B”.
Additional Information:
When l or c is present in an ac circuit, energy is required to build up the magnetic field around l or electric field in c. This energy comes from the source. However, power consumed in l or c is zero because all the power received from the source in a quarter cycle is returned to the source in the next quarter cycle. This power oscillates back and forth and is called reactive power. The total opposition to alternating current in an AC circuit is called impedance of the circuit Z.
Note:
1. Opposition offered by an inductor for the flow of ac is called ‘inductive reactance’.
2. An alternating voltage is one whose magnitude changes with time and direction changes periodically.
3. Frequency of direct current is zero. That is direct current is independent of frequency.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)