It was found that there are three types of low-energy arc discharge during the breaking process of resistive intrinsically safe circuits. For the first case, it is a typical case for low-energy arc discharge that arc power ascends to a maximum value and then descends to zero, arc discharge time is long and occurring probability is big. For the second case, it can explain why bigger sparks do not easily cause gas ignition while smaller sparks can cause gas ignition. Because arc power descends slowly all the way and arc power is smaller despite arc discharge time is long. For the third case, arc power is constant, arc discharge time and occurring probability is very small therefore causing no gas ignition. At last mathematical simulation was made using a current parabolic model.