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The equivalent inductance of a pair of a coupled inductor in various configuration are
(a) 7 H after series adding connection
(b) 1.8 H after series opposing connection
(c) 0.5 H after parallel connection with dotted terminal connected together.
(a) 7 H after series adding connection
(b) 1.8 H after series opposing connection
(c) 0.5 H after parallel connection with dotted terminal connected together.
The value of L1 L2 , and M are
- a)3 H, 1.6 H, 1.2 H
- b)1.6 H, 3 H, 1.4 H
- c)3.7 H, 0.7 H, 1.3 H
- d)2 H, 3 H, 3 H
Correct answer is option 'C'. Can you explain this answer?
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Equivalent Inductance of a Pair of Coupled Inductors
To find the equivalent inductance of a pair of coupled inductors in different configurations, we need to understand the concept of mutual inductance and how it affects the total inductance.
Mutual Inductance
Mutual inductance refers to the magnetic coupling between two inductors. When two inductors are placed close to each other, the magnetic field produced by one inductor induces a voltage in the other inductor. This phenomenon is known as mutual inductance.
The mutual inductance between two inductors is denoted by the symbol M and is measured in henries (H).
Series Adding Connection
When the two inductors are connected in series in the same direction, the equivalent inductance is given by:
L_eq = L1 + L2 + 2M
In this case, the equivalent inductance is 7 H. Let's denote the values of L1, L2, and M as X, Y, and Z, respectively.
X + Y + 2Z = 7 (Equation 1)
Series Opposing Connection
When the two inductors are connected in series in the opposite direction, the equivalent inductance is given by:
L_eq = L1 + L2 - 2M
In this case, the equivalent inductance is 1.8 H. Denoting the values as X, Y, and Z again, we have:
X + Y - 2Z = 1.8 (Equation 2)
Parallel Connection with Dotted Terminal Connected Together
When the two inductors are connected in parallel with the dotted terminals connected together, the equivalent inductance is given by:
L_eq = L1 + L2 + 2M
In this case, the equivalent inductance is 0.5 H. Denoting the values as X, Y, and Z again, we have:
X + Y + 2Z = 0.5 (Equation 3)
Solving the Equations
We now have a system of three equations (Equations 1, 2, and 3) with three unknowns (X, Y, and Z). We can solve these equations simultaneously to find the values of X, Y, and Z.
Adding equations 1 and 2, we get:
2X + 2Y = 8.8 (Equation 4)
Subtracting equation 3 from equation 1, we get:
2Z = 6.5 (Equation 5)
Solving equations 4 and 5, we find:
X = 3.7 H
Y = 0.7 H
Z = 1.3 H
Therefore, the values of L1, L2, and M are 3.7 H, 0.7 H, and 1.3 H, respectively. Thus, the correct answer is option C.
To find the equivalent inductance of a pair of coupled inductors in different configurations, we need to understand the concept of mutual inductance and how it affects the total inductance.
Mutual Inductance
Mutual inductance refers to the magnetic coupling between two inductors. When two inductors are placed close to each other, the magnetic field produced by one inductor induces a voltage in the other inductor. This phenomenon is known as mutual inductance.
The mutual inductance between two inductors is denoted by the symbol M and is measured in henries (H).
Series Adding Connection
When the two inductors are connected in series in the same direction, the equivalent inductance is given by:
L_eq = L1 + L2 + 2M
In this case, the equivalent inductance is 7 H. Let's denote the values of L1, L2, and M as X, Y, and Z, respectively.
X + Y + 2Z = 7 (Equation 1)
Series Opposing Connection
When the two inductors are connected in series in the opposite direction, the equivalent inductance is given by:
L_eq = L1 + L2 - 2M
In this case, the equivalent inductance is 1.8 H. Denoting the values as X, Y, and Z again, we have:
X + Y - 2Z = 1.8 (Equation 2)
Parallel Connection with Dotted Terminal Connected Together
When the two inductors are connected in parallel with the dotted terminals connected together, the equivalent inductance is given by:
L_eq = L1 + L2 + 2M
In this case, the equivalent inductance is 0.5 H. Denoting the values as X, Y, and Z again, we have:
X + Y + 2Z = 0.5 (Equation 3)
Solving the Equations
We now have a system of three equations (Equations 1, 2, and 3) with three unknowns (X, Y, and Z). We can solve these equations simultaneously to find the values of X, Y, and Z.
Adding equations 1 and 2, we get:
2X + 2Y = 8.8 (Equation 4)
Subtracting equation 3 from equation 1, we get:
2Z = 6.5 (Equation 5)
Solving equations 4 and 5, we find:
X = 3.7 H
Y = 0.7 H
Z = 1.3 H
Therefore, the values of L1, L2, and M are 3.7 H, 0.7 H, and 1.3 H, respectively. Thus, the correct answer is option C.
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