Answer & Solution
Answer: Option
C
Solution:
Self-inductance is a property of a coil that opposes changes in the current flowing through it.
Think of it like inertia for electricity!
Several factors affect how much self-inductance a solenoid (a coil of wire) has.
Let's break down why the correct answer is C: directly proportional to area of cross section.
The formula for self-inductance (L) of a solenoid is: L = (μ₀ * N² * A) / l
Where:
μ₀ = permeability of free space (a constant)
N = number of turns in the solenoid
A = area of cross-section of the solenoid
l = length of the solenoid
Now let's look at why the other options are wrong:
Option A: directly proportional to current flowing through the coil - Self-inductance itself doesn't depend on the current. It's a property of the coil, like its resistance. The *voltage* induced *does* depend on the *change* in current.
Option B: directly proportional to its length - The formula shows that self-inductance is *inversely* proportional to the length (l) of the solenoid, not directly proportional. If you make the solenoid longer, keeping everything else the same, the inductance decreases.
Option D: inversely proportional to area of cross-section - The formula clearly shows that self-inductance is *directly* proportional to the area of cross-section (A), not inversely proportional. A larger area allows for more magnetic flux to be created, increasing the inductance.
Therefore, the self-inductance of a solenoid is directly proportional to the area of its cross-section.
