In series circuits, all current goes through every load; there are no forks or branches in the circuit. So, the current, I1, through resistor, R1, and the current, I2, through resistor R2 are the same and equal to the current, I, of the circuit.
In series circuits the same current flows through all circuit components.
Just like pinching two places in the same hose results in less flow then pinching in only one place, the resistances of resistors in series add to give the total resistance of the circuit.
In accordance with the Law of Conservation of energy, the voltage drops across each resistor (the energy used by each resistor) add up to the voltage (energy) supplied by the source.
In summary, for series circuits,
ITOT = I1 = I2 = . . . .
RTOT = R1 + R2 + . . . .
VTOT = V1 + V2 + . . . .
2. In the diagram of a series circuit above, suppose R1 and R2 were light bulbs. If the light bulb at R2 burned out, what would happen to the brightness of the light bulb at R1?
3. Two resistors, 2.0 ohm and 3.0 ohm, are connected in series with a 12 V battery. Calculate: (a) the total resistance of the circuit; (b) the current leaving the battery; (c) the current through each resistor; (d) the voltage drop across each resistor.