Inductors are connected together in different ways in circuits, they can be connected end to end or side by side depending on their total inductance required.
There are two ways two or more inductors are connected together in circuits which are series and parallel. Inductors connected together side by side is called a series connection and if they are connected together end to end it is known as a parallel connection.
Parallel connection.
When inductors are connected together with one terminal of an inductor connected to another terminal of a inductor with the other terminals attached together is called a parallel connection, a typical example of this type of connection is shown above. When inductors are connected in parallel, the total inductance of all the inductors is lower than the least inductance of an inductor in the circuit. Mathematically we can calculate the total inductance with the formular, where L stands for induction. 1/(Ltotal)= 1/L1+1/L2+1/L3+1/L4+...
Example.
Calculate the total inductance of three inductors connected in parallel and each of 30H, 20H and 100H. Solution. Total inductance is calculated with the formular
1/(Ltotal)= 1/L1+1/L2+1/L3+1/L4+... Total inductance = 1/I total = 1/30+ 1/20 + 1/100 =0.033+0.05+0.01 =0.39 1/I total = 0.39
I total =2.564H.
You can observe that the total inductance is less than the least of them. When inductors are connected in parallel the current flowing through each of them isn't the same, but the voltage passing through each of them is the same.
Mutually coupled inductors in parallel.
When inductors are placed closed or near to each other, the magnetic field generated around their coils interferes with each other which affects their total inductance. Self inductance is the magnetic field induced into an inductor's coil when isolated or not in contact with another inductor. Mutual inductance is the magnetic field induced into two or more inductors placed near each other. When current carrying inductors are placed close to one another, the magnetic field generated interferes into one another either to reinforce their inductive power or to reduce it. There are two ways the total inductance is affected by mutual inductance which are parallel opposing and parallel aiding inductance. Parallel aiding inductance.
When inductors connected in parallel have their magnetic field touching each other with each inductors connected together in the same polarity, the total inductance is increased compared to zero mutual inductance inductors. The total inductance is calculated with the formular:
Example. Two inductors are connected in parallel aiding with each of 80H and 60H and a mutual inductance of 30H. Calculate the total inductance of the inductors.
Solution.
L-total=(L1L2-M^2)/(L1+L2-2M) =(80×60-30^2)/(80+60-2×30) = (4800-900)/(140-60) =(3900)/80
=48.75H.
Parallel opposing inductance.
Example.
Two inductors are connected in parallel opposing with each of 80H and 60H and a mutual inductance of 20H. Calculate the total inductance of the inductors.
Solution.
L-total= (L1L2-M^2)/(L1+L2+2M) = (80×60-20^2)/(80+60+2×20) = (4800-400)/(140+40)
= (4400)/(180)
=24.44H.
Series connection.
Inductors connected side by side one after the other is called a series connection. The same current flows through each of them because the current that flows through the first one also pass through the others, also the voltage across each of them isn't the same. The total inductance of inductors in series is more than the each of the inductor's inductance. Total inductance in series is calculated with the formular below.
L-TOTAL = L1+L2+L3+...
Example.
Three inductors of 10H, 20H and 40H are connected in series calculate the total inductance if there no mutal inductance.
Solution.
L-TOTAL = L1+L2+L3
=(10+20+40)H
=70H.
Mutually coupled inductors in series.
Inductors connected in series with their magnetic field touching each other exprience mutal inductance. The mutual inductance of inductors can either increase the total inductance or decrease it depending on how they are connected relative to one another. Series aiding connection. When inductors are connected that the lines of magnetic field produced are touching each other in same direction, this way the total inductance is increased. The total inductance of the circuit is calculated with the formula below. L-total = L1+L2+2M.
Example 1.
Two inductors 10H and 30H connected in series aiding and with a mutual inductance of 40H calculate the total inductance of the inductors.
Solution.
L-total = L1+L2+2M.
= 10+30+2(40)
= 40+80
=120H.
Example 2.
Three inductors 100H, 10H and 70H connected in series aiding and produced a total inductance of 500H Find the mutual inductance existing between them if they close to each other.
Solution.
L-total = L1+L2+L3+3M.
500 =100+10+70+3M.
500 =180+3M
500-180=3M
320=3M
M= 320/3
M=106.67H.
Series opposing connection.
When inductors are connected in series with their magnetic field touching in the opposite direction it reduces the total inductance. The total inductance is calculated with the formular below.
L total=L1+L2-2M.
Example 1.
Calculate the total inductance of two inductors of inductance 30H and 50H connected in series opposing with a mutual inductance of 12H.
Solution.
L total=L1+L2-2M
= 30+50-2(12)
= 80-24
=56H.
Example 2.
Three inductors 100H, 10H and 70H connected in series opposing and produced a total inductance of 30H Find the mutual inductance existing between them if they close to each other.
Solution.
L total=L1+L2+L3-3M =100+10+70-3×30
=180-90
=90H.
Tags:
Basic Electronics