33 µF, 35 V molded tantalum — the bulk capacitor for extreme-temperature rails
The TAJV336K035RNJ is a 33 µF, 35 V molded tantalum capacitor from the KYOCERA AVX TAJ series, in a surface-mount 2924 (7361 Metric) package with manufacturer size code V.
500 mOhm ESR — what it means for ripple and self-heating
The 500 mOhm ESR at 25°C sets the ripple current limit and the internal temperature rise. For a 100 kHz switching regulator output, the I²R loss at 1 A ripple current is 0.5 W — the 2924 body dissipates that with the board copper as the heatsink. A lower-ESR tantalum (e.g., 100 mOhm) would run cooler, but this ESR is typical for a 35 V rated part in this case size.