The only reason DMMs can't measure inductances is that it is more difficult to measure inductance than resistance or capacitance: this task requires special circuitry, which is not cheap. Since there are relatively few occasions when inductance measurements are required, standard DMMs do not have this functionality, which allows for lower cost.
Simple DMMs can measure capacitance by just charging the capacitor with a constant current and measuring the rate of voltage build-up. This simple technique provides surprisingly good accuracy and wide dynamic range, therefore it can be implemented in almost any DMM, without significant cost penalties. There are other techniques as well.
Theoretically, one could measure inductance by applying a constant voltage across an inductor and measuring the current build-up; however, in practice this technique is much more complicated to implement, and the accuracy is not that good as for capacitors due to the following reasons:
- Inductors may have relatively high parasitic resistance and capacitance
- Core losses (in cored inductors)
- EMI (incl. stray inductance and capacitance)
- Frequency dependent effects in inductors
- More
There are few techniques for measuring inductances (some of them are described here).
LCRs are special meters designed for inductance measurements and containing the required circuitry. These are costly tools.
Since the hardware for measuring the inductance may also be used for accurate measurement of R and C, LCRs also employ this circuitry in order to improve the accuracy of capacitance and resistance measurements (for example: AC resistance, AC capacitance, ESR etc.). I believe that the difference between measuring inductance and capacitance with LCR is just a matter of different firmware algorithms, though it is just a guess.
Therefore, the general answer to your question is "yes, LCRs are usually more accurate in RC measurements than DMMs, and they can measure a wider range of measurable quantities". However, this is just a rule of thumb - there are many superb DMMs and lousy LCRs out there... Read specs.
You could resonate it with a parallel or series capacitor and use a signal generator and o-scope for finding the resonant-frequency. You need to have a capacitor of at least 50 times it's likely self capacitance but, that can also be measured with a frequency generator and an o-scope. Then add a known capacitor (say 10nF) and you should see the resonant frequency drop at least ten if not 100 times. Use this formula: -
\$f_R = \dfrac{1}{2 \pi \sqrt{LC}}\$
I regularly build coils for transmitting power from fixed units to rotating electronics and the parallel resonance way is the most reliable for accuracy.
You should also note that depending on the material of the ferrite the inductance may change quite significantly with current passed through it - this is due to the onset of saturation but some ferrites are designed to be like this so, if possible try and run the test with an oscillator delivering enough voltage to impart the right amount of current into the coil.
Best Answer
There will be a small inductance created by wrapping up a cord in a loop, but the effect will be negligible. There are two reasons for this. First, the inductance will be so small that the effect at power line frequency is negligible. Second, power cords carry both the supply and return so the overall current flowing through the wire is zero, making the impact of any parasitic inductance negligible. Now, if you took 1000 ft. of wire for your hot and neutral and wrapped them up separately, you would definitely see some effects.