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Chapter 16: Problem 4

Two pure inductors, each of self-inductance \(L\) are connected in parallel but are well separated from each other, then the total inductance is (A) \(L\) (B) \(2 L\) (C) \(L / 2\) (D) \(L / 4\)

Short Answer

Expert verified
The total inductance of the two pure inductors, each with self-inductance L, connected in parallel is \(L_T = \frac{L}{2}\). The correct answer is option (C).

Step by step solution

01

Recall the formula for inductors in parallel

To determine the total inductance of two inductors connected in parallel, we can use the formula for parallel connections of inductors: \[ \frac{1}{L_T} = \frac{1}{L_1} + \frac{1}{L_2} \] where \(L_T\) is the total inductance, and \(L_1\) and \(L_2\) are the inductances of the two parallel inductors.
02

Apply the formula to our problem

Since both inductors have the same self-inductance L, we can substitute \(L_1 = L_2 = L\) into our formula: \[ \frac{1}{L_T} = \frac{1}{L} + \frac{1}{L} \]
03

Simplify the equation and solve for \(L_T\)

Combine the fractions on the right side of the equation: \[ \frac{1}{L_T} = \frac{2}{L} \] Now, to solve for \(L_T\), we can take the reciprocal of both sides: \[ L_T = \frac{L}{2} \]
04

Compare answer to given choices

Our calculated total inductance is \(L_T = \frac{L}{2}\). Looking at the four choices: (A) L (B) 2L (C) L/2 (D) L/4 The correct answer is option (C), \(L_T = \frac{L}{2}\).

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Most popular questions from this chapter

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