Imagine building a circuit with one battery and one resistor…

Imagine building a circuit with one battery and one resistor R.  Imagine now adding in series two more resistors of the same value R, in order to have a circuit with the same battery and three R resistors in series. The current through each resistor in the three-resistor circuit is the current through the resistor in the one-resistor circuit. The voltage across each resistor in the three-resistor circuit is the voltage across the resistor in the one-resistor circuit. The voltage of the battery in the three-resistor circuit is the voltage of the battery in the one-resistor circuit.