In a circuit with multiple resistors connected in series, how does the total resistance relate to the resistance of each resistor?

In a circuit with multiple resistors connected in series, how does the total resistance relate to the resistance of each resistor?

• A. It equals the product
• B. It equals the average
• C. It equals the sum
• D. It equals the inverse sum

Answer: (C)

In a series circuit, the same current flows through every resistor, and the voltages across each resistor add up to the total voltage. Ohm’s law tells us V = I·R. Since the current I is the same through all resistors and the total voltage is the sum of the individual voltages V1 + V2 + …, we have I·R_total = I·R1 + I·R2 + …, which simplifies to R_total = R1 + R2 + … + Rn. So the total resistance is the sum of the individual resistances. The other options don’t fit: multiplying would imply a different relationship, averaging would undercount, and the inverse-sum rule applies to parallel connections, not series.

In a series circuit, the same current flows through every resistor, and the voltages across each resistor add up to the total voltage. Ohm’s law tells us V = I·R. Since the current I is the same through all resistors and the total voltage is the sum of the individual voltages V1 + V2 + …, we have I·R_total = I·R1 + I·R2 + …, which simplifies to R_total = R1 + R2 + … + Rn. So the total resistance is the sum of the individual resistances. The other options don’t fit: multiplying would imply a different relationship, averaging would undercount, and the inverse-sum rule applies to parallel connections, not series.