Question

Write the unit of self-inductance.

Hint:

Think about the unit that follows from \(\varepsilon = -L\,dI/dt\); it is named after Joseph Henry.

Answer 1

Step 1: Recall the definition of self-inductance.
Self-inductance \(L\) links the induced EMF in a coil to the rate of change of current through it:
\[ \varepsilon = -L\,\frac{dI}{dt} \]

Step 2: Solve for the unit of L.
Rearranging, \( L = -\dfrac{\varepsilon}{dI/dt} \). So the unit is
\[ [L] = \frac{\text{volt}}{\text{ampere/second}} = \frac{\text{volt}\cdot\text{second}}{\text{ampere}} \]

Step 3: Name the SI unit.
This unit is called the henry (symbol H). Thus \(1\ \text{H} = 1\ \text{V}\cdot\text{s}\,/\,\text{A} = 1\ \text{Wb/A}\).

\[\boxed{\text{The SI unit of self-inductance is the henry (H).}}\]