Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store
seo-qna
SearchIcon
banner

Define the unit of self inductance

Answer
VerifiedVerified
487.8k+ views
like imagedislike image
Hint: Change in flux produces induced emf. If we are equating this induced emf and change in current through the coil, then the proportionality constant will be the self inductance.

Complete step by step answer:
As we know the flux is proportional to current.
ϕ=Li, where ϕ is the flux, L is the self inductance and i is the current.
Change in flux in a coil produces an induced emf. This is known as inductance effect. The induced emf is proportional to the rate of change of current through coil and this proportionality constant is called the self inductance.

e=Ldidt, where L is the self inductance, e is the induced emf and didt is the rate of change of current through the coil. The negative sign indicates that generated emf is opposing the cause producing it. Henry (H) is the SI unit of inductance.
Both self inductance and mutual inductance use the Henry to represent the inductance.

H=kgm2s2A2

One Henry can write like this also, one-kilogram meter squared per second square per ampere squared.

When a current change at the rate of 1 ampere per second and induced emf is one volt, the self inductance of the coil will be one Henry.

Additional information: We can find the self inductance of a solenoid.

Consider a solenoid of length l with n number of turns. If a current i flows through this solenoid, a magnetic field will generate inside.

Magnetic field, B=μ0Nil

Each turn have area A, then the total magnetic flux through the solenoid is given by; ϕB=μ0NilAN

i.e. ϕB=μ0N2ilA

Varying current will generate induced emf.

So, induced emf, e=ddt[μ0N2ilA]

Negative sign indicates the generated emf is opposing the cause producing it.

Constant terms can be taken outside, e=μ0N2Aldidt
These constant terms are collectively treated as proportionality constant and known as self inductance.

e=Ldidt

Therefore, L=μ0N2Al

L=μ0n2Al, where n is the number of turns (N) per unit length (l)

Note: Self inductance and mutual inductance are using the same unit Henry. One Henry can be written like this also; one-kilogram meter squared per second square per ampere squared.
Explore Offline
Centres