Because if the path is not closed , the circuit will break which will mean that between the two ends air is present. Since we know that air is an insulator . It will not allow the flow of charges though it and the current will not flow.
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r u sure closed path does not contain air????? bcoz air is present everywhere

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To allow electricity to a source...we need ti have a fixed path..insense we need the path to be if it is broken the electricity doesnt the path is disturbed...that means there is a gap between the path..hence electricity doesnt pass!! HOPE THIS HELPED