Students will use what they have learned from the previous lessons (ohm's law, resistors in series and resistors in parallel) and apply that knowledge to understand and solve more complicated resistor circuits.
Key Equations
Name  Electrical Symbol  Units  Analogy 

Voltage ( 
Volts 
A water dam with pipes coming out at different heights. The lower the pipe along the dam wall, the larger the water pressure, thus the higher the voltage. Examples: Battery, the plugs in your house, etc. 

Current ( 
Amps

A river of water. Objects connected in series are all on the same river, thus receive the same current. Objects connected in parallel make the main river branch into smaller rivers. These guys all have different currents. Examples: Whatever you plug into your wall sockets draws current 

Resistance ( 
Ohm 
If current is analogous to a river, then resistance is the amount of rocks in the river. The bigger the resistance the less current that flows Examples: Light bulb, Toaster, etc. 
Example 1
A more complicated circuit is analyzed.
Question: What is the total resistance of the circuit?
Answer: In order to find the total resistance we do it in steps (see pictures. First add the
Question: What is the total current coming out of the power supply?
Answer: Use Ohm’s Law
Question: What is the power dissipated by the power supply?
Answer:
Question: How much power is the
Answer: The
Question: If these resistors are light bulbs, order them from brightest to least bright.
Answer: The brightness of a light bulb is directly given by the power dissipated. So we could go through each resistor as we did the
We now know that the
Example 2
Watch this Explanation
Simulation
Circuit Construction Kit (DC Only) (PhET Simulation)
Explore More
 What will the ammeter read for the circuit shown to the right?
 You can use the simulation below to check your answer. Click on the blue arrow and select the part of the circuit you want to track. Then scroll down to the Data tab and you can see the current and voltage in different parts of the circuit.
Draw the schematic of the following circuit.
 Analyze the circuit below.
 Find the current going out of the power supply
 How many Joules per second of energy is the power supply giving out?
 Find the current going through the
75 Ω light bulb.  Find the current going through the
50 Ω light bulbs (hint: it’s the same, why?).  Order the light bulbs in terms of brightness
 If they were all wired in parallel, order them in terms of brightness.
 Find the total current output by the power supply and the power dissipated by the
20 Ω resistor.  You have a
600V power source, two10 Ω toasters that both run on100V and a25 Ω resistor. Show me how you would wire them up so the toasters run properly.
 What is the power dissipated by the toasters?
 Where would you put the fuses to make sure the toasters don’t draw more than 15 Amps?
 Where would you put a
25 Amp fuse to prevent a fire (if too much current flows through the wires they will heat up and possibly cause a fire)?
 Look at the following scheme of four identical light bulbs connected as shown. Answer the questions below giving a justification for your answer:
 Which of the four light bulbs is the brightest?
 Which light bulbs are the dimmest?
 Tell in the following cases which other light bulbs go out if:
 bulb
A goes out  bulb
B goes out  bulb \begin{align*}D\end{align*} goes out
 bulb
 Tell in the following cases which other light bulbs get dimmer, and which get brighter if:
 bulb \begin{align*}B\end{align*} goes out
 bulb \begin{align*}D\end{align*} goes out
 Refer to the circuit diagram below and answer the following questions.
 What is the resistance between \begin{align*}A\end{align*} and \begin{align*}B\end{align*}?
 What is the resistance between \begin{align*}C\end{align*} and \begin{align*}B\end{align*}?
 What is the resistance between \begin{align*}D\end{align*} and \begin{align*}E\end{align*}?
 What is the the total equivalent resistance of the circuit?
 What is the current leaving the battery?
 What is the voltage drop across the \begin{align*}12\ \Omega\end{align*} resistor?
 What is the voltage drop between \begin{align*}D\end{align*} and \begin{align*}E\end{align*}?
 What is the voltage drop between \begin{align*}A\end{align*} and \begin{align*}B\end{align*}?
 What is the current through the \begin{align*}25\ \Omega\end{align*} resistor?
 What is the total energy dissipated in the \begin{align*}25\ \Omega\end{align*} if it is in use for 11 hours?
 You are given the following three devices and a power supply of exactly \begin{align*}120\;\mathrm{v}\end{align*}. \begin{align*}^*\end{align*} Device \begin{align*}X\end{align*} is rated at \begin{align*}60\;\mathrm{V}\end{align*} and \begin{align*} 0.5\;\mathrm{A}\end{align*}\begin{align*}^*\end{align*} Device \begin{align*}Y\end{align*} is rated at \begin{align*}15\;\mathrm{w}\end{align*} and \begin{align*}0.5\;\mathrm{A}\end{align*}\begin{align*}^*\end{align*} Device \begin{align*}Z\end{align*} is rated at \begin{align*}120\;\mathrm{V}\end{align*} and \begin{align*}1800\;\mathrm{w}\end{align*} Design a circuit that obeys the following rules: you may only use the power supply given, one sample of each device, and an extra, single resistor of any value (you choose). Also, each device must be run at their rated values.
Answers to Selected Problems
 \begin{align*}0.5\mathrm{A}\end{align*}
 .
 a. \begin{align*}0.94 \;\mathrm{A}\end{align*} b. \begin{align*}112 \;\mathrm{W}\end{align*} c. \begin{align*}0.35 \;\mathrm{A}\end{align*} d. \begin{align*}0.94 \;\mathrm{A}\end{align*} e. \begin{align*}50, 45, 75 \ \Omega\end{align*} f. both \begin{align*}50 \ \Omega\end{align*} resistors are brightest, then \begin{align*}45 \ \Omega\end{align*}, then \begin{align*}75 \ \Omega\end{align*}
 a. \begin{align*}0.76 \;\mathrm{A}\end{align*} b. \begin{align*}7.0 \;\mathrm{W}\end{align*}
 b. \begin{align*}1000 \;\mathrm{W}\end{align*}
 .
 a. \begin{align*}9.1 \ \Omega\end{align*} b \begin{align*}29.1 \ \Omega\end{align*} c. \begin{align*}10.8 \ \Omega\end{align*} d.\begin{align*} 26.8 \ \Omega\end{align*} e. \begin{align*}1.8\mathrm{A}\end{align*} f. \begin{align*}21.5\mathrm{V}\end{align*} g. \begin{align*}19.4\mathrm{V}\end{align*} h. \begin{align*}6.1\mathrm{V}\end{align*} i. \begin{align*}0.24\mathrm{A}\end{align*} j. \begin{align*}16 \;\mathrm{kW}\end{align*}
 .