Chapter 30: Q49P (page 899)

The inductor arrangement of Figure, with
$L_{1} = 30.0 mH, L_{2} = 50.0 mH, L_{3} = 20.0 {mHandL}_{4} = 15.0 mH$ is to be connected to a varying current source. What is the equivalent inductance of the arrangement?

Short Answer

Expert verified

$L_{e q} = 59.3 m H$

Step by step solution

Given

$L_{1} = 30.0 m H; L_{2} = 50.0 m H; L_{3} = 20.0 m H; L_{4} = 15.0 m H$

Understanding the concept

Equivalent inductance forinductors connected in series isthesum of all inductances. And reciprocal of equivalent inductance for parallel connection of inductances isthesum of reciprocals of inductances.

Formulae:

Equivalent inductance forinductors connected inparallel is

$\frac{1}{L_{e q}} = \sum_{n = 1}^{N} \frac{1}{L_{n}}$

Equivalent inductance forinductors connected inseries is

$L_{e q} = \sum_{n = 1}^{N} L_{n}$

Calculate the equivalent inductance of the arrangement

$L_{2}$ and $L_{3}$ are connected in parallel, so their equivalent is given by

$\frac{1}{L_{23}} = \frac{1}{L_{2}} + \frac{1}{L_{3}} \frac{1}{L_{23}} = \frac{1}{50} + \frac{1}{20}$

Hence,

$L_{23} = 14.3 m H$

Now, $L_{23}, L_{1} a n d L_{4}$ are in series.

$L_{e q} = L_{1} + L_{23} + L_{4} L_{e q} = 30 + 14.3 + 15 L_{e q} = 59.3 m H_{z}$

Therefore the equivalent inductance = 59.6mH

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The inductor arrangement of Figure, with
$L_{1} = 30.0 mH, L_{2} = 50.0 mH, L_{3} = 20.0 {mHandL}_{4} = 15.0 mH$ is to be connected to a varying current source. What is the equivalent inductance of the arrangement?

Short Answer

Step by step solution

Given

Understanding the concept

Calculate the equivalent inductance of the arrangement

One App. One Place for Learning.

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The inductor arrangement of Figure, withL1=30.0mH,L2=50.0mH,L3=20.0mHandL4=15.0mHis to be connected to a varying current source. What is the equivalent inductance of the arrangement?

Short Answer

Step by step solution

Given

Understanding the concept

Calculate the equivalent inductance of the arrangement

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Torque and Rotational Motion

Quantum Physics

Electromagnetism

Physics of Motion

Electricity

Magnetism and Electromagnetic Induction

Study anywhere. Anytime. Across all devices.

The inductor arrangement of Figure, with
$L_{1} = 30.0 mH, L_{2} = 50.0 mH, L_{3} = 20.0 {mHandL}_{4} = 15.0 mH$ is to be connected to a varying current source. What is the equivalent inductance of the arrangement?