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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.
The value of L1 ,L2 and M 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.
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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Coupled Inductors
Coupled inductors are a pair of inductors that are magnetically linked together. The mutual inductance between the two inductors is denoted by M. The equivalent inductance of a pair of coupled inductors depends on the configuration of the connection.
Series Adding Connection
When the two inductors are connected in series with the same polarity, the equivalent inductance is the sum of the individual inductances and twice the mutual inductance.
L_eq = L1 + L2 + 2M
Given that the equivalent inductance is 7 H, we can write the equation as:
7 = 3 + 1.6 + 2M
Solving for M, we get:
M = 1.2 H
Series Opposing Connection
When the two inductors are connected in series with opposing polarity, the equivalent inductance is the difference between the individual inductances and twice the mutual inductance.
L_eq = abs(L1 - L2) - 2M
Given that the equivalent inductance is 1.8 H, we can write the equation as:
1.8 = abs(3 - 1.6) - 2M
Solving for M, we get:
M = 0.5 H
Parallel Connection
When the two inductors are connected in parallel with the same polarity, the equivalent inductance is given by:
1/L_eq = 1/L1 + 1/L2 + 2/M
Given that the equivalent inductance is 0.5 H and the dotted terminal is connected together, we can write the equation as:
1/0.5 = 1/3 + 1/1.6 + 2/M
Solving for M, we get:
M = 1.3 H
Therefore, the values of L1, L2, and M are 3.7 H, 0.7 H, and 1.3 H respectively, which is option 'C'.
Coupled inductors are a pair of inductors that are magnetically linked together. The mutual inductance between the two inductors is denoted by M. The equivalent inductance of a pair of coupled inductors depends on the configuration of the connection.
Series Adding Connection
When the two inductors are connected in series with the same polarity, the equivalent inductance is the sum of the individual inductances and twice the mutual inductance.
L_eq = L1 + L2 + 2M
Given that the equivalent inductance is 7 H, we can write the equation as:
7 = 3 + 1.6 + 2M
Solving for M, we get:
M = 1.2 H
Series Opposing Connection
When the two inductors are connected in series with opposing polarity, the equivalent inductance is the difference between the individual inductances and twice the mutual inductance.
L_eq = abs(L1 - L2) - 2M
Given that the equivalent inductance is 1.8 H, we can write the equation as:
1.8 = abs(3 - 1.6) - 2M
Solving for M, we get:
M = 0.5 H
Parallel Connection
When the two inductors are connected in parallel with the same polarity, the equivalent inductance is given by:
1/L_eq = 1/L1 + 1/L2 + 2/M
Given that the equivalent inductance is 0.5 H and the dotted terminal is connected together, we can write the equation as:
1/0.5 = 1/3 + 1/1.6 + 2/M
Solving for M, we get:
M = 1.3 H
Therefore, the values of L1, L2, and M are 3.7 H, 0.7 H, and 1.3 H respectively, which is option 'C'.
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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.The value of L1 ,L2 and M area)3 H, 1.6 H, 1.2 Hb)1.6 H, 3 H, 1.4 Hc)3.7 H, 0.7 H, 1.3 Hd)2 H, 3 H, 3 HCorrect answer is option 'C'. Can you explain this answer?
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