What happens to the total resistance when more resistors are added in series?

When additional resistors are added in series to a circuit, the total resistance increases. This occurs because the total resistance in a series circuit is the sum of the individual resistances. Adding more resistors means that there are more pathways that the electric current must navigate, and each resistor adds its resistance to the total.

Mathematically, the total resistance (R_total) can be calculated using the formula:

[ R_{total} = R_1 + R_2 + R_3 + ... + R_n ]

where R_1, R_2, R_3, ..., R_n are the resistances of each individual resistor. With every additional resistor, you are effectively increasing the total value, resulting in a higher total resistance.

This principle is fundamental in understanding series circuits and is important for applications where control of current flow is required, as increasing total resistance will reduce the overall current in the circuit according to Ohm's Law (I = V/R).