Question 205: Electromagnetic Induction

Question

A coil of wire of radius ' $r$ ' has 600 turns and a self-inductance of 108 mH . The self-inductance of a coil with same radius and 500 turns is

Accepted Answer

Step 1: Recall the dependence of self-inductance
For a given geometry (same core, radius, length, etc.), the self-inductance scales as
$ L \propto N^{2} $
where $N$ is the number of turns.
Step 2: Set up ratio
Given:
$N_1 = 600$, $L_1 = 108 \,	ext{mH}$
$N_2 = 500$, $L_2 = ?$
So,
$ \frac{L_2}{L_1} = \left(\frac{N_2}{N_1}ight)^2 $
$ L_2 = L_1 \left(\frac{N_2}{N_1}ight)^2 $
Step 3: Substitute values
$ L_2 = 108 	imes \left(\frac{500}{600}ight)^2 $
$ \frac{500}{600} = \frac{5}{6} $
$ \left(\frac{5}{6}ight)^2 = \frac{25}{36} $
$ L_2 = 108 	imes \frac{25}{36} $
$ = 3 	imes 25 = 75 \, 	ext{mH} $
Ã¢ÂÂ Final Answer:
The self-inductance is
Option B: 75 mH

Answer

80 mH

Answer

75 mH

Answer

108 mH

Answer

90 mH

Electromagnetic Induction

A coil of wire of radius ' r ' has 600 turns and a self-inductance of 108 mH . The self-inductance of a coil with same radius and 500 turns is

Choose the correct answer: