The equation $r_{total} = r_1 + r_2 + r_3$ describes the total resistance in a series circuit, where resistors are connected end-to-end. In a series circuit, the total resistance increases as more resistors are added, since the current must pass through each resistor sequentially, resulting in a cumulative effect on the overall resistance faced by the current. This fundamental relationship is crucial for understanding how circuits behave when resistors are arranged in series.
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