The primary objective of this work is the analysis and interpretation of co
ronal observations of Capella obtained in 1999 September with the High Ener
gy Transmission Grating Spectrometer on the Chandra X-ray Observatory and t
he Extreme Ultraviolet Explorer (EUVE). He-like lines of O (O vii) are used
to derive a density of 1.7 x 10(10) cm(-3) for the coronae of the binary,
consistent with the upper limits derived from Fe xxi, Ne ix and Mg xi line
ratios. Previous estimates of the electron density based on Fe xxi should b
e considered as upper limits. We construct emission measure distributions a
nd compare the theoretical and observed spectra to conclude that the corona
l material has a temperature distribution that peaks around 4-6 MK, implyin
g that the coronae of Capella were significantly cooler than in the previou
s years. In addition, we present an extended line list with over 100 featur
es in the 5-24 Angstrom wavelength range, and find that the X-ray spectrum
is very similar to that of a solar flare observed with SMM. The observed to
theoretical Fe xvii 15.012-Angstrom line intensity reveals that opacity ha
s no significant effect on the line flux. We derive an upper limit to the o
ptical depth, which we combine with the electron density to derive an upper
limit of 3000 km for the size of the Fe xvii emitting region. In the same
context, we use the Si iv transition region lines of Capella from HST/Godda
rd High-Resolution Spectrometer observations to show that opacity can be si
gnificant at T = 10(5) K, and derive a path-length of approximate to 75 kin
for the transition region. Both the coronal and transition region observat
ions are consistent with very small emitting regions, which could be explai
ned by small loops over the stellar surfaces.