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

Thursday, May 22, 2014

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

Hello!

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, $\displaystyle\delta{U}={I}{R}.$ The constant $\displaystyle{R}$ is called the resistance of the conductor.

When some $\displaystyle{n}$ resistors of the resistances $\displaystyle{R}_{{i}}$ are connected in series, the same electrical current $\displaystyle{I}$ flows successively through each of them. And each resistor causes the voltage drop proportional to its resistance $\displaystyle{R}_{{i}}:$ $\displaystyle\delta{U}_{{i}}={R}_{{i}}{I}.$ Together, all resistors cause the voltage drop of $\displaystyle{\left({R}_{{1}}+{R}_{{2}}+\ldots+{R}_{{n}}\right)}{I},$ which, in turn, means that the total resistance of a chain is $\displaystyle{R}_{{1}}+{R}_{{2}}+\ldots+{R}_{{n}}.$