Reduced to base SI units, one henry is the equivalent of one kilogram meter squared per second squared per ampere squared (kg m2 s-2 A-2).
This does not look like the standard F = ma formula for a force but there is a mass term. What does the mass term represent? I am trying to understand how the units gel together.
Best Answer
Let \$P\$ be power in watts, \$I\$ be current in amps, \$W\$ be work in Joules,
\$A\$ Acceleration in meters per \$\text{second}^2\$ \$D\$ distance in meters, \$M\$ Mass in kg.
\$T\$ Time in seconds, \$F\$ Force in newtons and \$V\$ voltage in volts.
We know \$ P = V \cdot I\$ so \$V = \dfrac{P}{I}\$.
Basic physics should tell you Power is Work divided by time \$P = \dfrac{W}{T}\$.
Work is Force times distance \$W = F \cdot D\$
Force is mass times Acceleration \$F = M \cdot A\$.
Putting all this together we see.
\$ V = \dfrac{P}{I} = \dfrac{W}{I \cdot T} = \dfrac{F \cdot D}{I \cdot T} = \dfrac{M \cdot A \cdot D}{I \cdot T} = \dfrac{M \cdot D \cdot D}{I \cdot T \cdot T^2} = \dfrac{M \cdot D^2}{I \cdot T^3}\$
Using standard SI units the volt is therefore \$\dfrac{\mathrm{kg} \cdot \mathrm{m}^2}{\mathrm{A} \cdot \mathrm{s}^3}\$
Now we know \$ V = L \cdot \dfrac{\text{d}I}{\text{d}t}\$ Now dimensionally \$ L = \dfrac{\text{volts}}{\text{amps}} \cdot \text{time}\$
Using standard SI units the henry is therefore \$\dfrac{\mathrm{kg} \cdot \mathrm{m}^2}{\mathrm{A} \cdot \mathrm{s}^3} \cdot \dfrac{\text{s}}{\text{A}} = \dfrac{\mathrm{kg} \cdot \mathrm{m}^2}{\mathrm{A}^2 \cdot \mathrm{s}^2}\$