Chapter 21, Problem 88GP

To determine

To find the wire of a tightly wound solenoid is unwound and used to make another tightly wound solenoid of twice the diameter.

Answer to Problem 88GP

Solution:

The rounding inductance changes by a factor of 2.

Explanation of Solution

Given info:

$L$ is new inductance, $A$ is new area of cross-section and $l$ is new length.

Formula used:

$L=\mu N^{2}A/l$

Calculation:

The expression for reactance of an inductor is given as

$X_L=\omega L\mathrm{............}\left(1\right)$

$\begin{array}{l}L=\mu N^{2}A/l\\ =4\times A\\ =l/2\\ =2\times L\end{array}$