DC Circuits, Part 2: Encountering Resistance

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In Part 1, we learned about the conventions used to describe direct current flowing through a circuit, and the batteries used to drive that current. In Part 2, we’re investigating resistance.

Resistance inhibits the flow of charge in a circuit by converting electrical energy to heat; resistors are the devices that provide resistance. They’re typically denoted by zig-zag lines on circuit diagrams:
Perhaps it’s not surprising to learn that resistance is a function of the the material a resistor is made of and its shape. The former point is pretty straightforward: We would expect smaller resistance in wires made of conductors and larger resistance in wires made of insulators. As for the latter point, longer wires have larger resistance, and wider wires have smaller resistance. The units of resistance are ohms.

It takes work to move charges through a resistor, and this is accomplished through conversion of electric potential energy into work. Keep in mind that circuits are powered by batteries that provide the electric potential energy (measured in voltage, which is electric potential energy per unit charge). When current flows from a battery through a resistor, the conversion of electric potential energy into work is manifested by a drop in electric potential energy from one side of the resistor to the other side. This is measured as a “voltage drop.” Voltmeters can be hooked up to circuits in parallel to resistors to measure such voltage drops. (For a great explanation for why resistors in parallel cause the same voltage drops, see The Physics Classroom’s explanation, which is about halfway down the page: http://www.physicsclassroom.com/class/circuits/Lesson-4/Parallel-Circuits.)
A given circuit may have multiple resistors, arranged in series and/or in parallel. Resistors in series produce additive resistance, as all charges in a current must pass through each resistor.
For n resistors in series, the effective resistance (as if they were combined into one resistor) is given by:
resistor series
Resistors in parallel produce resistance in a more complex way. This is because only some charges in a current will pass through any given resistor, but the voltage drop must be the same for each resistor in parallel.
For n resistors in parallel, the effective resistance (as if they were combined into one resistor) is given by:
resistor parallel
This relationship for resistors in parallel can be derived using Ohm’s Law in concert with Kirchhoff’s Laws – check out this great explanation from the University of Guelph: https://www.physics.uoguelph.ca/tutorials/ohm/Q.ohm.intro.parallel.html.

Resistance has a negative connotation, but it isn’t bad – any device that you have hooked up to a circuit (such as a light-bulb) is a resistor, and the drop in electric potential is what runs it! Furthermore, resistors convert electric energy into thermal energy. Light-bulbs have so much resistance compared to other common devices that they warm up enough to emit visible light! Hair dryers, toasters, stoves, the heater in your car – they all heat up due to resistance, and our lives are better for it. We measure the amount of thermal energy generated by resistors through voltage drops by measuring power. Power has units of Joules per second, usually called watts. So when you look at the wattage of any device, you’re looking at the amount of thermal energy produced every second under normal conditions! The equation for power is:
So there you have it: Despite their names, resistors make our lives easier! In Part 3, we’ll investigate capacitors. Once we have those three basic ingredients (batteries, resistors, capacitors), we’ll put them together in simple and multi-loop circuits.

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