Self-Induction — Question 9

Question 9

An integrated terminal measurement separates inductance from winding resistance

A coil has unknown constant L and known winding resistance r=4.00 ohms. Over a measured interval, its current increases by 2.00 A. The measured integrals are $\int vdt=.300$ V s and $\int i dt=.0200$ A s. Use passive voltage.

1. Infer L without assuming a linear current ramp.

2. Find the erroneous estimate obtained by ignoring resistance and its relative error.

Question 9 - Solution

An integrated terminal measurement separates inductance from winding resistance

(a) Method and calculation

$$v=ri+L\dot i\Rightarrow\int vdt=r\int i dt+L\Delta i.$$$$\boxed{L=\frac{.300-(4.00)(.0200)}{2.00}=.110\,H}.$$

(b) Interpretation and further calculation

$$L_{\mathrm{naive}}=.300/2.00=.150\,H.$$$$\boxed{(L_{\mathrm{naive}}-L)/L=4/11=36.3636\%}.$$

Physical check

The resistive voltage-time area must be subtracted; neither the detailed current waveform nor its pointwise derivative is needed.