The self inductance of a coil is L. Keeping the length and area same, the number of turns in the coil is increased to four times. The self inductance of the coil will now be
Question
The self inductance of a coil is L. Keeping the length and area same, the number of turns in the coil is increased to four times. The self inductance of the coil will now be
Solution
The self-inductance (L) of a coil is directly proportional to the square of the number of turns (N) in the coil. This relationship can be expressed as L ∝ N².
If the number of turns in the coil is increased to four times, the new number of turns will be 4N.
Substituting this into the relationship, the new self-inductance (L') will be L' ∝ (4N)² = 16N².
Since L ∝ N², we can say that L = kN², where k is a constant of proportionality.
Therefore, L' = 16kN² = 16L.
So, if the number of turns in the coil is increased to four times, the self-inductance of the coil will increase to sixteen times.
Similar Questions
The self inductance L of a solenoid of length l and area of cross-section A, with a fixed number of turns N increases asl and A increasel decreases and A increasesl increases and A decreasesboth l and A decrease
The magnetic flux linked with a coil changes by 2×10-2Wb when the currentchanges by 0.01A. The self inductance of the coil is
A thin coil has 10 rectangular turns of wire. When a current of 2.00 A runs through the coil, there is a total flux of 0.005 T-m2 enclosed by one turn of the coil (note that the inductance is the proportionality constant between current and magnetic flux). What is the total inductance in Henries?
The current in a coil changes from 2 A to 10 A in 80 ms. As a result, an e.m.f of 5.0V is induced in the coil. Determine the magnitude of the self-inductance of the coil
The electric current in a circular coil of four turns produces a magnetic induction 32 T at its centre. The coil is unwound and is rewound into a circular coil of single turn, the magnetic induction at the centre of the coil by the same current will be :8 T4 T2 T16 T
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.