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Question: The equivalent inductance of two inductors is 2.4 H when connected in parallel and 10 H when connect...

The equivalent inductance of two inductors is 2.4 H when connected in parallel and 10 H when connected in series. What is the value of inductances of the individual inductors?

A

8 H, 2 H

B

6 H, 4 H

C

5 H, 5 H

D

7 H, 3 H

Answer

6 H, 4 H

Explanation

Solution

In series connection

L1+L2=10H\mathrm { L } _ { 1 } + \mathrm { L } _ { 2 } = 10 \mathrm { H }….. (i)

And parallel connection

L1 L2( L1+L2)=2.4H\frac { \mathrm { L } _ { 1 } \mathrm {~L} _ { 2 } } { \left( \mathrm {~L} _ { 1 } + \mathrm { L } _ { 2 } \right) } = 2.4 \mathrm { H }… (ii)

Substituting the value of (L1+L2)\left( \mathrm { L } _ { 1 } + \mathrm { L } _ { 2 } \right) from (i) into

(ii), we get

L1 L2=(2.4)(L1+L2)=2.4×10=24\mathrm { L } _ { 1 } \mathrm {~L} _ { 2 } = ( 2.4 ) \left( \mathrm { L } _ { 1 } + \mathrm { L } _ { 2 } \right) = 2.4 \times 10 = 24

…… (iii)

Solving (i) and (iii), we get

L1=6H,L2=4H\mathrm { L } _ { 1 } = 6 \mathrm { H } , \mathrm { L } _ { 2 } = 4 \mathrm { H }