When you have a series loop of devices connected across the battery . . .
-- The individual voltages across each device in the series loop all add up to the voltage of the battery.
-- The individual voltages divide up according to the resistance of each device in the loop. One with larger resistance has more voltage across it. One with smaller resistance has less voltage across it.
-- And again ... they all add up to the battery voltage.
(Also, by the way, although you didn't ask . . . . . The current in the series loop is the same at every point.)
the emf of the battery excludes the internal resistance - the voltage across the bulb includes this
In a series circuit, the voltage output of the battery is the total sum of the voltages across each bulb. Voltage is divided among the bulbs based on their resistance, with bulbs of equal resistance sharing the battery voltage equally. The current remains constant throughout the circuit.
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