How to calculate induced current?
i want to know why do we use ohm's law in calculating the induced
  current ?


Current isn’t induced; voltage is induced as per Faraday’s law of induction and, as a result of voltage being induced (by the changing magnetic field), then the current that may flow is defined by the induced voltage and the impedance of the circuit i.e. Ohm’s law. 

At DC use resistance and for an AC induced voltage use the reactance and resistance and remember to consider that the wire in which the voltage is induced has self-inductance.