'current-induced' is a modern English compound formed from 'current' + 'induced'. 'current' ultimately comes from Latin 'currere' (via Old French/Middle English), where the root meant 'to run', and 'induced' comes from Latin 'inducere', where 'in-' meant 'into' and 'ducere' meant 'to lead'.

'current' evolved from Latin 'currere' to Old French forms (e.g. 'corant') and into Middle English as 'current', while 'induced' derives from Latin 'inducere' → past participle 'inductus' → Middle English forms and modern English 'induce/induced'.

Originally 'current' referred generally to 'running' or 'a running flow' and 'induce' meant 'to lead into'; over time they came to be used in technical senses (e.g. electrical current, and 'to cause'), yielding the compound meaning 'caused by a flow/current'.