Three cells of \(1.5 \mathrm{~V}, 2.5 \mathrm{~V}\) and \(3.5 \mathrm{~V}\) respectively are connected in series to form a battery. Find the e.m.f of the battery.

When multiple cells are connected in series, this means that the positive terminal of one cell is connected to the negative terminal of the next. This setup is common when you need a higher voltage than what one cell can provide. In a series connection, the total electromotive force (e.m.f) of the battery is the sum of the individual e.m.fs of all the cells connected.

imagine you're stringing beads on a necklace, with each bead representing a cell. By connecting one after the other, the length of the necklace (equivalent to the total e.m.f) increases with each bead (cell) added. This simplicity allows for easy calculations of the overall voltage output of the battery, which is particularly useful when the cells have different voltages, as seen in our example exercise.

Electromotive force, commonly abbreviated as e.m.f, is a term used to describe the energy provided by a cell or battery to drive a unit charge around a complete circuit. It's the 'push' or 'force' that sets the electrons in motion and can be thought of as the battery's ability to do work on a charge. However, despite the name, it is not actually a force but a potential difference, measured in volts.

A helpful analogy might be to consider e.m.f as a pump in a water circuit, where it provides the energy to move water through the pipes (the circuit). Without this 'pump' or driving energy, the electrons in a circuit wouldn't flow, and no electrical work could be done. This concept is central to understanding how batteries power devices, as seen in the textbook exercise.

Calculating parameters in series circuits follows straightforward rules due to the nature of the series connection. In such circuits, the current remains constant throughout, but the voltage can vary across different components. When dealing with e.m.fs, as in our exercise, you sum all the individual voltages (or e.m.fs) to find the total provided by the battery or cell combination.

It's important to note that while the total e.m.f is the sum of the individual e.m.fs, the internal resistance of the cells, if provided, must also be considered, which will slightly lower the overall voltage available from the battery. For a series circuit involving resistors, the total resistance would be the sum of the individual resistances, which directly affects the flow of current according to Ohm's Law.

Voltage is the measure of the potential difference between two points in an electrical field and is the driving force behind the movement of electrons through a circuit. It is analogous to water pressure in a pipe; the higher the pressure, the stronger the water flows. In electrical terms, the higher the voltage, the greater the potential for current to flow (assuming resistance is constant).

It dictates how much potential energy is available to be converted into other forms, such as kinetic energy, heat, or light. Understanding voltage is essential when studying series circuit calculations and electromotive force. It helps to clarify how different cells with varying voltages contribute to the overall e.m.f of a battery when connected in series, as demonstrated in the original exercise.