What effect does adding a third resistor in series have on the total resistance of a circuit with two resistors?

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When a third resistor is added in series to a circuit that already has two resistors, it impacts the total resistance of the circuit. In a series configuration, the total resistance is the sum of the resistances of all the resistors. Therefore, if you have two resistors with resistances R1 and R2, the total resistance (R_total) is given by the formula R_total = R1 + R2.

When a third resistor, R3, is added in series, the new total resistance becomes R_total = R1 + R2 + R3. This clearly indicates that the total resistance increases because you are adding the resistance value of the third resistor to the existing total. Each additional resistor in series contributes more resistance, making it harder for current to flow through the circuit.

This fundamental principle of resistances in series is a key concept in circuit theory, emphasizing how the configuration of resistors impacts the overall resistance in a circuit.