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Two coils have inductances of 8 mH and 18 mH and a coefficient of coupling of 0.5. If the two coils are connected in series aiding, the total inductance will be
Answer & Solution
Correct Answer:
Option
B
Let's break down this problem to understand how to calculate the total inductance of two coils connected in series aiding!
First, let's define some key terms:
* Inductance (L): A coil's ability to store energy in a magnetic field, measured in Henries (H). In our case, L1 = 8 mH and L2 = 18 mH.
* Coefficient of Coupling (k): A number between 0 and 1 that describes how effectively the magnetic field of one coil links with the other. Here, k = 0.5. A value of 1 means perfect coupling.
* Mutual Inductance (M): The inductance due to the interaction of the magnetic fields of the two coils. It's how much one coil's current affects the voltage in the other coil.
The formula for Mutual Inductance (M) is: M = k * sqrt(L1 * L2)
Let's calculate M: M = 0.5 * sqrt(8 mH * 18 mH) = 0.5 * sqrt(144 mH²) = 0.5 * 12 mH = 6 mH
When coils are connected in series aiding (also known as series cumulative), their magnetic fields add up.
The formula for the total inductance (L_total) in series aiding is: L_total = L1 + L2 + 2M
Now, let's plug in the values: L_total = 8 mH + 18 mH + 2 * 6 mH = 8 mH + 18 mH + 12 mH = 38 mH
Therefore, the total inductance will be 38 mH. The correct answer is Option B.
First, let's define some key terms:
* Inductance (L): A coil's ability to store energy in a magnetic field, measured in Henries (H). In our case, L1 = 8 mH and L2 = 18 mH.
* Coefficient of Coupling (k): A number between 0 and 1 that describes how effectively the magnetic field of one coil links with the other. Here, k = 0.5. A value of 1 means perfect coupling.
* Mutual Inductance (M): The inductance due to the interaction of the magnetic fields of the two coils. It's how much one coil's current affects the voltage in the other coil.
The formula for Mutual Inductance (M) is: M = k * sqrt(L1 * L2)
Let's calculate M: M = 0.5 * sqrt(8 mH * 18 mH) = 0.5 * sqrt(144 mH²) = 0.5 * 12 mH = 6 mH
When coils are connected in series aiding (also known as series cumulative), their magnetic fields add up.
The formula for the total inductance (L_total) in series aiding is: L_total = L1 + L2 + 2M
Now, let's plug in the values: L_total = 8 mH + 18 mH + 2 * 6 mH = 8 mH + 18 mH + 12 mH = 38 mH
Therefore, the total inductance will be 38 mH. The correct answer is Option B.
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LoginM=k under root L1L2
Ltotal = 8+18+2(6)=38
m = k × √L1 L2
m = 0.5 × √8 × 18
m = 0.5 × √ 144 = 0.5 × 12
m = 6
To find total inductance
L = L1 + L2 + 2M
L = 8 + 18 + 2 ( 6)
L = 8 +18 + 12
L = 38 henry
m=k*sqrt(L1.L2)=0.5*sqrt(8*18)=0.5*12=6
L=8+18+2*6=38mH
mutual inductance = K*route of L1 AND L2