The core of a coil has a length of 200 mm. The inductance of the coil is 6 mH. If the core length is doubled, all other quantities remaining the same, the inductance will be?
Understand the Problem
The question is asking about the effect of changing the core length of a coil on its inductance, given that all other quantities remain constant. It provides an initial inductance value and requires the calculation of the new inductance after doubling the length of the core.
Answer
$3 \, \text{mH}$
Answer for screen readers
The new inductance will be $3 , \text{mH}$.
Steps to Solve
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Understanding Inductance and Core Length Inductance ($L$) of a coil is inversely proportional to its core length ($l$) when all other factors are held constant. This relationship can be expressed as: $$ L \propto \frac{1}{l} $$
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Identifying Initial Values The initial inductance ($L_1$) is given as 6 mH and the initial core length ($l_1$) is 200 mm.
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Doubling the Core Length If the core length is doubled, the new length ($l_2$) becomes: $$ l_2 = 2 \times 200 , \text{mm} = 400 , \text{mm} $$
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Calculating New Inductance Using the inverse relationship of inductance and core length: $$ \frac{L_1}{L_2} = \frac{l_2}{l_1} $$
Substituting the known values: $$ \frac{6 , \text{mH}}{L_2} = \frac{400 , \text{mm}}{200 , \text{mm}} $$
This simplifies to: $$ \frac{6 , \text{mH}}{L_2} = 2 $$
- Solving for New Inductance Rearranging gives: $$ L_2 = \frac{6 , \text{mH}}{2} = 3 , \text{mH} $$
The new inductance will be $3 , \text{mH}$.
More Information
When the core length of a coil is doubled, the inductance is reduced by half, assuming all other factors remain constant. This principle is important in understanding how inductors behave in circuits.
Tips
- Neglecting the inverse relationship between inductance and core length.
- Misinterpreting the doubling of the length as doubling the inductance instead of reducing it.
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