Resistors in Series and Parallel Circuits

When we talk about a "series circuit", we are talking about objects that are placed consecutively in the path of current flow. For this lesson, a series circuit will contain two or more resistors placed sequentially in a circuit:

An example is that old string of Christmas lights you may still have lying around: when one bulb went out, they all went out because the path for current flow was interrupted. In our circuit, there is a voltage drop across each resistor, but the current flow through the circuit is constant. Thus,

I1 = I2 = I3 = Itot but Vtot = V1 + V2 +V3

If we define Req as the Equivalent Resistance in a circuit, or what the circuit would see if we turned all of the resistors into one big resistor, then from Ohm's Law:

IReq = I1R1 + I2R2 + I3R3

But since all currents are equal,

Req = R1 + R2 + R3

When resistors are added in series, the Equivalent Resistance is the sum of the values of the individual resistors. Series equivalent resistance will always be greater than any individual resistance. In our example,

Req = 1W + 3 W + 2 W = 6 W, so

What is the voltage drop across each resistor?

V1 = IR1 = (2A)(1 W) = 2V

V2 = IR2 = (2A)(3 W) = 6V

V3 = IR3 = (2A)(2 W) = 4V

Vtot = V1 + V2 + V3 = 12 V which checks against our battery voltage.

When batteries are connected in series, the effective voltages add as well.

A parallel circuit consists of 2 or more elements wired in parallel, like your house wiring or the type of Christmas lights we buy today. A fault or interruption in one branch will still allow current to flow through other branches, so if one bulb goes out, the rest stay lit. When resistors are arranged in parallel with an energy source, such as a battery, the potential difference (voltage) across each resistor and the potential difference across the energy source are always equal.

Note: Since V is the same at the same node points across all branches, the potential drop across both resistors must be the same. Also,

Itot = I1 + I2

and

Vtot = V1 = V2

Therefore, from Ohm's Law:

or for a more generalized case,

Note that as more resistors are added in parallel, the total resistance of the circuit goes down. In fact, the total resistance will always be less than the smallest resistance. In our example,

And

Also, unlike series circuits, connecting batteries in parallel has no effect on total
voltage. That is, as long as the batteries all have the same voltage!

Try the following for additional study:

http://micro.magnet.fsu.edu/electromag/java/ohmslaw/index.html

http://micro.magnet.fsu.edu/electromag/java/resistor/index.html

http://science.howstuffworks.com/power2.htm
(A great website on power generation)

http://www.saburchill.com/physics/chapters/0082.html

Some coding tips and interesting facts about resistors at:

http://www.williamson-labs.com/resistors.htm

More about Ohm’s law some sample problems, and a simulated experiment at: http://www.physics.uoguelph.ca/tutorials/ohm/Q.ohm.intro.html

For Practice Problems, Try: Giancoli Multiple Choice Practice Questions (Go ahead - try a few.)