Inductance is the ratio of the magnetic flux in an inductor, Φ, to the current through the inductor, I.
Eric Murray, Fall 2006
Inductance is the ratio of the magnetic flux in an inductor, Φ, to the current through the inductor, I.
L = Φ/I
Unfortunately, the magnetic flux is difficult to measure.
On the other hand, if a sinusoidally varying electric potential is applied across an inductor, a sinusoidally varying current will flow through it. The inductive reactance is the ratio of the potential amplitude, V0, to the current amplitude, I0. The inductive reactance, XL, depends on the frequency of the applied potential, f, as XL = ωL, where ω is the angular frequency, ω = 2πf. It is analogous to resistance:
XL = V0/I0 or V0 = I0XL
The potential amplitude is on the vertical axis and the current amplitude is on the horizontal axis purely as a matter of convenience. Remember that the potential is the cause of the current.
When a constant electric potential difference is suddenly applied across a circuit consisting of an inductor and a resistor in series, the potential difference across the inductor, ΔVL, the potential difference across the resistor, ΔVR, and the current in the circuit, I, all vary with time, t. There is a characteristic time, τ, called the time constant. For example, the current varies with time according to
I = I0(1 - e-t/τ) = I0 - I0e-t/τ
where I0 is the current at time t = 0, the instant the switch is closed.
To determine τ, you will fit the current vs. time graph to a general exponential decay curve,
I = Ae-Bt + y0
where A, B, and y0 are fit parameters. The fit parameter B is related to the time constant by τ = 1/B. The inductance L is related to the time constant by τ = L/R.