The Spectrum uses a 'power connector', probably 2.5mm (but I've not measured it). The central pin of the part on the PCB is -ve, and the outer of the plug (cable mounted part) is therefore +ve. The ZX81 uses a 3.5mm jack socket (what you call a 'phone socket' across the Pond) for the power input. The tip is +ve and the sleeve is -ve.