What is the formula for the total resistance of two resistors in series?

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Multiple Choice

What is the formula for the total resistance of two resistors in series?

Explanation:
When resistors are connected in series, the same current flows through both, and the voltages across them add up to the total voltage. Using Ohm’s law, the voltages are V1 = I·R1 and V2 = I·R2, so the total voltage is V_total = V1 + V2 = I(R1 + R2). The total resistance seen by the source is R_total = V_total / I = I(R1 + R2) / I = R1 + R2. So the combined resistance in series is simply the sum of the two resistances. The other formulas correspond to different setups—parallel resistance is (R1·R2)/(R1+R2), and the square-root expression isn’t the appropriate rule for combining resistors in these basic configurations.

When resistors are connected in series, the same current flows through both, and the voltages across them add up to the total voltage. Using Ohm’s law, the voltages are V1 = I·R1 and V2 = I·R2, so the total voltage is V_total = V1 + V2 = I(R1 + R2). The total resistance seen by the source is R_total = V_total / I = I(R1 + R2) / I = R1 + R2. So the combined resistance in series is simply the sum of the two resistances. The other formulas correspond to different setups—parallel resistance is (R1·R2)/(R1+R2), and the square-root expression isn’t the appropriate rule for combining resistors in these basic configurations.

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