Answer

Verified

63.9k+ views

**Hint:**When inductor connected in series combination then equivalent inductance will be given as

${L_{eq}} = {L_1} + {L_2} + {L_3} + ....$

When inductors are connected in parallel combination then equivalent inductance will be given as

$\dfrac{1}{{{L_{eq}}}} = \dfrac{1}{{{L_1}}} + \dfrac{1}{{{L_2}}} + \dfrac{1}{{{L_3}}} + .....$

**Step by step answer:**Given that 2 inductors ${L_1}$ and ${L_2}(Let)$ are connected in parallel then their equivalent inductance is 2.4 mH.

i.e., $\dfrac{1}{{{L_{eq}}}} = \dfrac{1}{{{L_1}}} + \dfrac{1}{{{L_2}}}$

So, \[\dfrac{1}{{{L_1}}} + \dfrac{1}{{{L_2}}} = \dfrac{1}{{2.4}}\]

$\dfrac{{{L_2} + {L_1}}}{{{L_1}{L_2}}} = \dfrac{{10}}{{24}}$

${L_1}{L_2} = \dfrac{{24}}{{10}}({L_1} + {L_2})$ …..(1)

When ${L_1}$ and ${L_2}$ are connected in series then their equivalent inductance is 10 mH.

i.e., ${L_{eq}} = {L_1} + {L_2}$

$10 = {L_1} + {L_2}$ …..(2)

From equation 1 & 2 we get

${L_1}{L_2} = \dfrac{{24}}{{10}} \times 10$

${L_1}{L_2} = 24$

So, ${L_1} = \dfrac{{24}}{{{L_2}}}$ …..(3)

On putting the value of ${L_1}$ in equation 2

$\dfrac{{24}}{{{L_2}}} + {L_2} = 10$

$\dfrac{{24 + L_2^2}}{{{L_2}}} = 10$

$24 + L_2^2 = 10{L_2}$

$L_2^2 - 10{L_2} + 24 = 0$

$L_2^2 - 6{L_2} - 4{L_2} + 24 = 0$

${L_2}({L_2} - 6) - 4({L_2} - 6) = 0$

$({L_2} - 6)({L_2} - 4) = 0$

${L_2} = 4,6$ ….(4)

Now put the value of ${L_2}$ in equation 3

We will get ${L_1}$.

Here we have 2 values of ${L_2}$. So, put one by one each value and will get ${L_1}$.

When ${L_2} = 4mH$

Then from equation 3

${L_1} = \dfrac{{24}}{4}$

${L_1} = 6mH$ …..(6)

When ${L_2} = 6mH$

Then from equation 3

${L_1} = \dfrac{{24}}{6}$

${L_1} = \dfrac{{24}}{6}$

${L_1} = 4mH$ …..(6)

So, we will get 2 combinations of ${L_1}$ & ${L_2}$ which are

If ${L_1} = 4mH$ If ${L_1} = 6mH$

Then ${L_2} = 6mH$ then ${L_2} = 4mH$

Now, we have to calculate the difference between ${L_1}$ and ${L_2}$. Which is

${L_1} - {L_2} = 6 - 4 = 2mH$

So, from both combinations of ${L_1}$ and ${L_2}$ we will get a difference between them of 2 mH.

Hence, option B is the correct answer. 2mH

**Note:**In many problems of inductors, they can ask for current and voltage.

In series combination, the value of current in each inductor is the same. But voltage is different.

In parallel combination, the potential difference i.e., voltage across each inductor is same but current is different.

Recently Updated Pages

Write a composition in approximately 450 500 words class 10 english JEE_Main

Arrange the sentences P Q R between S1 and S5 such class 10 english JEE_Main

What is the common property of the oxides CONO and class 10 chemistry JEE_Main

What happens when dilute hydrochloric acid is added class 10 chemistry JEE_Main

If four points A63B 35C4 2 and Dx3x are given in such class 10 maths JEE_Main

The area of square inscribed in a circle of diameter class 10 maths JEE_Main

Other Pages

A boat takes 2 hours to go 8 km and come back to a class 11 physics JEE_Main

If a wire of resistance R is stretched to double of class 12 physics JEE_Main

Differentiate between homogeneous and heterogeneous class 12 chemistry JEE_Main

Electric field due to uniformly charged sphere class 12 physics JEE_Main