Is henry the SI unit of mutual inductance?
2 Answers
Yes, the henry (symbol: H) is the SI unit of mutual inductance. To understand this, let's break it down:
### What is Mutual Inductance?
Mutual inductance is a measure of how effectively a changing magnetic field created by one coil induces a voltage in a nearby coil. This phenomenon is based on Faraday's Law of Induction, which states that a change in magnetic flux through a coil induces an electromotive force (EMF) in that coil. When you have two coils close to each other, the changing magnetic field in one coil can induce a voltage in the other coil. The efficiency of this induction is quantified by mutual inductance.
### The Unit: Henry (H)
- **Definition**: One henry is defined as the amount of mutual inductance between two coils when a change of one ampere per second in the current through one coil induces a voltage of one volt in the other coil. In mathematical terms:
\[
M = \frac{V}{\frac{dI}{dt}}
\]
where:
- \( M \) is the mutual inductance in henries,
- \( V \) is the induced voltage in volts,
- \(\frac{dI}{dt}\) is the rate of change of current in amperes per second.
- **Dimensions**: In terms of fundamental SI units, one henry is equivalent to one ohm-second (Ω·s). Its dimensional formula is:
\[
[H] = [M][L^2][T^{-2}][I^{-2}]
\]
where:
- \( [M] \) is mass,
- \( [L] \) is length,
- \( [T] \) is time,
- \( [I] \) is electric current.
### Practical Understanding
In practical terms, if you have two inductors (coils) with a mutual inductance of 1 henry, a change in current of 1 ampere per second in one coil will induce a voltage of 1 volt in the other coil. The henry thus quantifies how effectively the magnetic field of one coil links with another.
So, in summary, the henry is indeed the SI unit used to measure mutual inductance, reflecting how efficiently one coil's changing magnetic field induces a voltage in a neighboring coil.
### What is Mutual Inductance?
Mutual inductance is a measure of how effectively a changing magnetic field created by one coil induces a voltage in a nearby coil. This phenomenon is based on Faraday's Law of Induction, which states that a change in magnetic flux through a coil induces an electromotive force (EMF) in that coil. When you have two coils close to each other, the changing magnetic field in one coil can induce a voltage in the other coil. The efficiency of this induction is quantified by mutual inductance.
### The Unit: Henry (H)
- **Definition**: One henry is defined as the amount of mutual inductance between two coils when a change of one ampere per second in the current through one coil induces a voltage of one volt in the other coil. In mathematical terms:
\[
M = \frac{V}{\frac{dI}{dt}}
\]
where:
- \( M \) is the mutual inductance in henries,
- \( V \) is the induced voltage in volts,
- \(\frac{dI}{dt}\) is the rate of change of current in amperes per second.
- **Dimensions**: In terms of fundamental SI units, one henry is equivalent to one ohm-second (Ω·s). Its dimensional formula is:
\[
[H] = [M][L^2][T^{-2}][I^{-2}]
\]
where:
- \( [M] \) is mass,
- \( [L] \) is length,
- \( [T] \) is time,
- \( [I] \) is electric current.
### Practical Understanding
In practical terms, if you have two inductors (coils) with a mutual inductance of 1 henry, a change in current of 1 ampere per second in one coil will induce a voltage of 1 volt in the other coil. The henry thus quantifies how effectively the magnetic field of one coil links with another.
So, in summary, the henry is indeed the SI unit used to measure mutual inductance, reflecting how efficiently one coil's changing magnetic field induces a voltage in a neighboring coil.