Which of the following is the smallest in size and can amplify electrical signals?

The correct choice is a transistor because it is a semiconductor device that can amplify electrical signals and is known for its compact size. Transistors are widely used in electronic circuits for signal amplification and switching, making them essential components in modern electronics. Their small form factor allows for dense integration in devices, contributing to miniaturization in technology.

In contrast, a battery serves as a power source by storing and providing electrical energy but does not amplify signals. A switch is a device used to either make or break connections in an electrical circuit; it simply opens or closes a circuit without amplification. A relay is also a type of switch that uses an electromagnet to control the opening and closing of contacts but tends to be larger and is not primarily used for amplifying signals. Hence, the transistor stands out as the smallest device capable of amplifying electrical signals.