What Happens To Resistance In Series?
The simplest kind of combination of multiple circuit elements has resistors connected in series (figure below).
The rule is easy: to find the resistance of a series combination of resistors, add their individual resistances.
For example, if a 10-ohm resistor is connected in series with a 20-ohm resistor, their combined resistance is 30 ohm. This means that we could replace the two resistors with a single resistor of 30 ohm and make no difference whatsoever to the rest of the circuit.
In fact, if the series resistors were enclosed in a box with only the terminal ends sticking out, there would be no way for us to tell by electrical testing on the terminals whether the box contained a single 30-ohm resistor or any series combination of two or more resistors whose resistances added up to 30 ohm.
Thus, an arbitrary number of resistances can be added in series, and their order does not matter.
Intuitively, the addition rule makes sense because if we think of a resistor as posing an “obstacle” to the current, and note that the same current must travel through each element in the series, each obstacle adds to the previous ones.
This notion can be formalized in terms of voltage drop. Across each resistor in a series combination, there will be a voltage drop proportional to its resistance. It is always true that, regardless of the nature of the elements (whether they are resistors or something else), the voltage drop across a set of elements connected in series equals the sum of voltage drops across the individual elements.
This notion reappears in the context of Kirchhoff’s Voltage Law.
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