Answer

Verified

451.5k+ views

Hint: The formula for series and parallel condition of inductance is similar to that of resistance. In series the inductance is the sum of inductance and in parallel resultant inductance is the sum of the reciprocal of individual inductance.

Complete step by step answer:

To proceed further, let us know about Inductance and its types.

Inductance: We know that the magnetic flux in any conductor is directly proportional to the current.

\[{{\phi }_{B}}\propto I\]

Where, \[{{\phi }_{B}}\] is the magnetic flux and \[I\]is the current.

\[\begin{align}

& N{{\phi }_{B}}\propto I \\

& N{{\phi }_{B}}=LI \\

\end{align}\]

Where, \[N\] is the number of turns in the induction coil. And here \[L\] is the constant which is the ratio of net flux to the electric current and is known as Inductance.

Inductance is a scalar quantity and its SI unit is Henry or H.

In series: When two coils of inductance \[{{L}_{1}}\] and \[{{L}_{2}}\]connected in series. Then inductance will add:

\[{{L}_{series}}={{L}_{1}}+{{L}_{2}}\]

In Parallel: When two coils of inductance \[{{L}_{1}}\] and \[{{L}_{2}}\]connected in parallel. Then reciprocal of inductance will add:

\[\dfrac{1}{{{L}_{parallel}}}=\dfrac{1}{{{L}_{1}}}+\dfrac{1}{{{L}_{2}}}\]

In our question it is given that:

\[\begin{align}

& {{L}_{parallel}}=2.4H \\

& {{L}_{series}}=10H \\

\end{align}\]

Let \[{{L}_{1}}\]and \[{{L}_{2}}\]be the two individual inductor, therefore:

\[\begin{align}

& \dfrac{1}{{{L}_{1}}}+\dfrac{1}{{{L}_{2}}}=\dfrac{1}{2.4} \\

& \dfrac{1}{{{L}_{1}}}+\dfrac{1}{{{L}_{2}}}=\dfrac{10}{24} \\

& \dfrac{{{L}_{1}}+{{L}_{2}}}{{{L}_{1}}{{L}_{2}}}=\dfrac{10}{24} \\

\end{align}\]

Also,

\[{{L}_{1}}+{{L}_{2}}=10\]

Or

\[{{L}_{2}}=10-{{L}_{1}}\]

And,

\[\begin{align}

& \dfrac{10}{{{L}_{1}}{{L}_{2}}}=\dfrac{10}{24} \\

& {{L}_{1}}{{L}_{2}}=24 \\

\end{align}\]’

\[\begin{align}

& {{L}_{1}}(10-{{L}_{1}})=24 \\

& {{L}^{2}}_{1}-10{{L}_{1}}+24=0 \\

& ({{L}_{1}}-6)({{L}_{1}}-4)=0 \\

& {{L}_{1}}=6,{{L}_{1}}=4 \\

\end{align}\]

Or

\[{{L}_{2}}=6,{{L}_{2}}=4\]

Hence the inductance of two individual inductors are \[6H\]and \[4H\] respectively.

Therefore the correct answer is option B.

Additional Information:

Types of Inductance: There are two types of Inductance.

Self Inductance: When current passing through the coil changes, magnetic flux also changes hence induced EMF is produced in the same coil. This phenomenon is called self inductance.

Mutual Inductance: When the current changes in a coil, then flux linked with the other coil placed near the first changes. Hence an induced current is produced in the second coil. This phenomenon is called mutual inductance.

The first coil in which current changes is called primary coil and the coil in which flux changes is called secondary coil.

The function of a transformer is based on the principle of mutual induction.

Note: If the question is objective type as of above. Then students can directly put the values of options to the condition of parallel and series. You will get the answer quickly. Let us see how:

The sum of every value in options gives us \[10H\]which will not give us the right answer. Now let's put the condition in parallel.

\[{{L}_{parallel}}=\dfrac{{{L}_{1}}{{L}_{2}}}{{{L}_{1}}+{{L}_{2}}}\]

Option B, is satisfying the above relation. Hence option B is correct.

Complete step by step answer:

To proceed further, let us know about Inductance and its types.

Inductance: We know that the magnetic flux in any conductor is directly proportional to the current.

\[{{\phi }_{B}}\propto I\]

Where, \[{{\phi }_{B}}\] is the magnetic flux and \[I\]is the current.

\[\begin{align}

& N{{\phi }_{B}}\propto I \\

& N{{\phi }_{B}}=LI \\

\end{align}\]

Where, \[N\] is the number of turns in the induction coil. And here \[L\] is the constant which is the ratio of net flux to the electric current and is known as Inductance.

Inductance is a scalar quantity and its SI unit is Henry or H.

In series: When two coils of inductance \[{{L}_{1}}\] and \[{{L}_{2}}\]connected in series. Then inductance will add:

\[{{L}_{series}}={{L}_{1}}+{{L}_{2}}\]

In Parallel: When two coils of inductance \[{{L}_{1}}\] and \[{{L}_{2}}\]connected in parallel. Then reciprocal of inductance will add:

\[\dfrac{1}{{{L}_{parallel}}}=\dfrac{1}{{{L}_{1}}}+\dfrac{1}{{{L}_{2}}}\]

In our question it is given that:

\[\begin{align}

& {{L}_{parallel}}=2.4H \\

& {{L}_{series}}=10H \\

\end{align}\]

Let \[{{L}_{1}}\]and \[{{L}_{2}}\]be the two individual inductor, therefore:

\[\begin{align}

& \dfrac{1}{{{L}_{1}}}+\dfrac{1}{{{L}_{2}}}=\dfrac{1}{2.4} \\

& \dfrac{1}{{{L}_{1}}}+\dfrac{1}{{{L}_{2}}}=\dfrac{10}{24} \\

& \dfrac{{{L}_{1}}+{{L}_{2}}}{{{L}_{1}}{{L}_{2}}}=\dfrac{10}{24} \\

\end{align}\]

Also,

\[{{L}_{1}}+{{L}_{2}}=10\]

Or

\[{{L}_{2}}=10-{{L}_{1}}\]

And,

\[\begin{align}

& \dfrac{10}{{{L}_{1}}{{L}_{2}}}=\dfrac{10}{24} \\

& {{L}_{1}}{{L}_{2}}=24 \\

\end{align}\]’

\[\begin{align}

& {{L}_{1}}(10-{{L}_{1}})=24 \\

& {{L}^{2}}_{1}-10{{L}_{1}}+24=0 \\

& ({{L}_{1}}-6)({{L}_{1}}-4)=0 \\

& {{L}_{1}}=6,{{L}_{1}}=4 \\

\end{align}\]

Or

\[{{L}_{2}}=6,{{L}_{2}}=4\]

Hence the inductance of two individual inductors are \[6H\]and \[4H\] respectively.

Therefore the correct answer is option B.

Additional Information:

Types of Inductance: There are two types of Inductance.

Self Inductance: When current passing through the coil changes, magnetic flux also changes hence induced EMF is produced in the same coil. This phenomenon is called self inductance.

Mutual Inductance: When the current changes in a coil, then flux linked with the other coil placed near the first changes. Hence an induced current is produced in the second coil. This phenomenon is called mutual inductance.

The first coil in which current changes is called primary coil and the coil in which flux changes is called secondary coil.

The function of a transformer is based on the principle of mutual induction.

Note: If the question is objective type as of above. Then students can directly put the values of options to the condition of parallel and series. You will get the answer quickly. Let us see how:

The sum of every value in options gives us \[10H\]which will not give us the right answer. Now let's put the condition in parallel.

\[{{L}_{parallel}}=\dfrac{{{L}_{1}}{{L}_{2}}}{{{L}_{1}}+{{L}_{2}}}\]

Option B, is satisfying the above relation. Hence option B is correct.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Give a reason for the establishment of the Mohammedan class 10 social science CBSE

What are the two main features of Himadri class 11 social science CBSE

The continent which does not touch the Mediterranean class 7 social science CBSE

India has form of democracy a Direct b Indirect c Presidential class 12 sst CBSE

which foreign country is closest to andaman islands class 10 social science CBSE

One cusec is equal to how many liters class 8 maths CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Which foreign country is closest to Andaman Islands class 11 social science CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE