When resistors are connected in series does total resistance decrease or increase?

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The answer is increases. Now let's figure out why.

Ohm's law states that the current through a conductor is directly proportional to the voltage, or, in other words, that the voltage drop between endpoints of a conductor is directly proportional to the current, `Delta U = I R.` The constant `R` is called the resistance of the conductor.

When some `n` resistors of the resistances `R_i` are connected in series, the same electrical current `I` flows successively through each of them. And each resistor causes the voltage drop proportional to its resistance `R_i:`  `Delta U_i = R_i I.` Together, all resistors cause the voltage drop of `(R_1 + R_2 + ... + R_n) I,` which, in turn, means that the total resistance of a chain is `R_1 + R_2 + ... + R_n.`

Note that a resistance is always positive, so a sum is always greater than any summand.

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