What is the total resistance in a series circuit with multiple resistors connected end-to-end?

What is the total resistance in a series circuit with multiple resistors connected end-to-end?

• A. It is equal to the largest resistance.
• B. It is the product of the resistances.
• C. It is the sum of the individual resistances.
• D. It is the reciprocal of the sum of reciprocals.

Answer: (C)

In a series arrangement, all components carry the same current, and the voltages across them add up to the total supply voltage. Because the current is the same through each resistor, the total resistance the source “feels” is simply the sum of all the individual resistances. That makes the total resistance equal to the sum of the values involved. For example, a 2 Ω resistor in series with a 3 Ω resistor gives a total of 5 Ω. The other options don’t fit because the total is not determined by the largest resistance, and you don’t multiply resistances in series. The reciprocal of the sum of reciprocals is the parallel-formula, not for series circuits.

In a series arrangement, all components carry the same current, and the voltages across them add up to the total supply voltage. Because the current is the same through each resistor, the total resistance the source “feels” is simply the sum of all the individual resistances. That makes the total resistance equal to the sum of the values involved. For example, a 2 Ω resistor in series with a 3 Ω resistor gives a total of 5 Ω. The other options don’t fit because the total is not determined by the largest resistance, and you don’t multiply resistances in series. The reciprocal of the sum of reciprocals is the parallel-formula, not for series circuits.