The ubiquitous nature of electricity makes an electrical fault a primary consideration at the start of almost every fire investigation. Principal amongst the types of faults that can cause a fire is the resistive heating fault. While methods for calculating the maximum power transfer from a supply to a load are well known to electrical engineers, especially in the fields of radio and audio engineering, their useful application for fire investigation has not been explored publicly. A power transfer relationship is re-worked here by considering the original circuit as the supply and the fault as the load. This results in the 'quarter-power equation' for application in fire investigation, which can help to assess whether this particular means of ignition, the resistive heating fault, is viable for the case being investigated. This article provides analysis and guidance on the derivation, use and limitations of the 'quarter-power equation' and shows how it was useful in eliminating a possible cause of fire under consideration in a particular investigation.