If a live wire inside the appliance touches a neutral wire, a very big current passes between the two wires at the point of contact. This is called a short circuit. Provided the fuse blows, it cuts the current off.
Even if an appliance is switched off, never touch the wires inside the supply cable. People's bodies are at zero volts. If someone touches a live wire, a big potential difference will act across their body, causing a current to flow through them. They will suffer an electric shock, which could be lethal.
How the metal case of an electrical appliance is connected to earth
The earth wire in the mains cable is connected to the longest pin in the plug, which is then connected to the metal case of the appliance to provide a safe path to earth
Sockets and plug cases are made of stiff plastic materials that enclose the electrical connections. Plastic is used because it is a good electrical insulator.
Each coulomb of charge leaves the battery with 12J of energy, transfers 10J of energy to the torch bulb, and transfers 2J of energy to the variable resistor