The heat produced in conducting wire is given by joules law as,
H=I2Rt
i ) The amount of heat produced in current conducting wire, is proportional to the square of the amount of current that is flowing through the circuit, when the electrical resistance of the wire and the time of current flow is constant.
ie H∝I2 (when R, t are constant)
II) Heat generated due to the flow of current is proportional to the time of current flow, when the electrical resistance and amount of current flow is constant.
ie H∝t (when I,R are constant)
III) The amount of heat produced is proportional to the electrical resistance of the wire when the current in the circuit and the time of current flow is constant.
ie H∝R (when I, t are constant)