What is the reason for the output voltage being lower than the input voltage on a battery charger?

The output voltage being lower than the input voltage on a battery charger can be attributed to the design of the charger, specifically in relation to the transformer used within it. When a transformer steps down voltage, it does so by having fewer turns of wire in the secondary winding compared to the primary winding. This turns ratio is what determines the voltage output in accordance with the formula ( V_{out} = V_{in} \times \frac{N_{sec}}{N_{pri}} ), where ( N_{sec} ) and ( N_{pri} ) are the number of turns in the secondary and primary coils, respectively.

If the secondary windings have fewer turns than the primary, the output voltage is inherently reduced. This design is essential for charging batteries, as most batteries operate at a lower voltage than the supply.

In contrast, factors like a fully discharged battery, a malfunctioning charger, or compatibility with higher voltages do not intrinsically lead to a lower output voltage as a result of design. While these other conditions might affect charging performance or safety, the relationship of turns in the transformer accurately explains the steady-state voltage reduction observed.