Series and parallel resistances pg. 51 This lesson presents the equations for calculating total (equivalent) resistance for series and parallel combinations of resistors, and provides practice in calculating total resistance. In the hands-on investigation, students combine lamps in series and parallel, and relate the effect on lamp brightness to the circuit’s total resistance.

Objectives Physics terms Calculate the equivalent resistance for resistors connected in both series and parallel combinations. Construct series and parallel circuits of lamps (resistors). Observe and explain relative lamp brightness in series and parallel circuits. series circuit parallel circuit equivalent resistance The next set of slides will preview the assessments for the first objective. Objectives two and three will be assessed within the investigation itself.

Series circuits have only one pathway No options Parallel Circuit Series circuits have only one pathway No options Parallel circuits have multiple pathways Have options I I I V V

Impact of Resistors A B C The battery and the resistors in these circuits are identical. What is different about these circuits? A B C I1 I2 I3 A least resistance, most current C  most resistance, least current Ask “What must be true about the current through each of these resistors? (Answer: the same amount of current must flow through each resistor in series.) Try to get the students to come up with the answer to the question on the slide.

Equivalent resistance Take a second & think about what each of those words mean. What does equivalent mean? What does resistance mean? So that means equivalent resistance means: Equal/same How hard it is for current to get through/resistance to current This is the definition of equivalent resistance. -Equal difficulty for current to get through. -It’s how much resistance a single resistor would have to have to replace multiple resistors in a circuit

Look at these 2 circuits. What would the equivalent resistance of the second circuit need to be to equal the resistance of the first circuit? 3R This is an example of equivalent resistance. Again, we are assuming that the voltage source is the same, and all resistors are identical. If they have the same resistance, what can you say about the current in each circuit? Same in both

Finding Equivalent resistance in series circuits To find the equivalent resistance add up the individual resistances: Notes to remember for finding Req for series: -Current has to go through every resistor in the circuit so: Add em up WHOLE When you add resistors in series, the total resistance INCREASES. Therefore, when you add resistors in series, the current DECREASES. This is because each resistor added in series makes it harder for the current to flow along that branch.

Ex.1 What is the Req of each circuit? Review the use of Ohm’s law. V= IR so I = V/R Req = 10 Ω Req = 15 Ω Adding resistors in series makes the total resistance increase.

Ex.2 How much current flows? Point out that Ohm’s law can be applied to a single resistor, or a combination of resistors with an equivalent resistance. I = 1 A I = .67 A

Equivalent Resistance Practice Series 1. A 10 Ω resistor, a 15 Ω resistor, and a 5 Ω resistor are connected in series. What is the equivalent resistance of this arrangement? 2. Two strings of tree lights, each with a resistance of 150 Ω, are connected together in series. What is the Req? 3. When you add resistors in series does Req increase or decrease? 4. Does total current increase or decrease when you add resistors?

Finding equivalent resistance in parallel circuits To find the Req you must add the inverse of the resistances: Notes to remember for finding Req for parallel: -Current has choices so: Add em up as FRACTIONS When you add resistors in parallel, the equivalent resistance DECREASES and total current INCREASES. So to find the equivalent resistance of resistors in parallel, we cannot simply add up the values. We need a new formula, shown here.

Equivalent resistance: parallel If you have two 4 Ω resistors in parallel, what is the equivalent resistance? A. ½ Ω B. 2 Ω C. 4 Ω D. 8 Ω Don’t forget to flip the fraction at the end! Point out that the answer, 2 ohms, is on the bottom. The answer is 2 ohms, not ½ ohm. Forgetting to flip the fraction is a very common error when adding resistors in parallel.

Practice What is the Req of each circuit? These are all 10 Ω resistors. Answers on next slide. Req = 10 Ω Req = 5 Ω Req = 3.3 Ω Adding resistors in parallel makes the total resistance decrease.

Practice How much current flows? Point out that the current through EACH resistor is 3 amps. If there are three resistors in parallel, there are 9 amps total.

Parallel circuits In the circuit with parallel resistors: total current flow doubles because total resistance is halved. Analogies are helpful in getting this point across. It is like adding lanes to a highway so that the vehicles can flow What is the Req for the parallel circuit? R 2R ½ R

Equivalent Resistance Practice Parallel 1. A 10 Ω resistor and a 15 Ω resistor are connected in parallel. What is the Req of this arrangement? 2. Two strings of lights, each with a resistance of 150 Ω, are connected together. What is the Req when the strings are connected in parallel? If possible, shows students how easy it is to solve these problems by using the inverse (x^-1) button on their calculators.

What are the voltage drops across each resistor in both circuits? Voltage drops in series 10 V drop 20 V drop 10 V drop What are the voltage drops across each resistor in both circuits? Compare these two circuits. Note that that in the circuit on the right, the voltage of the battery must be shared between the two resistors. The battery “pumps up” the energy of the charges. The charges lose half their electrical potential energy in the first resistor (10 V), and the other half the energy in the second resistor (10 V) for a total voltage drop of 20 volt.

What are the voltage drops across each resistor in both circuits? Voltage drops in parallel 4 A 4 A 20 V drop 20 V drop 20 V drop What are the voltage drops across each resistor in both circuits? Each resistor is directly connected to the two ends of the battery, so each resistor is exposed to the full 20 V of the battery. The current splits, so each resistor gets only 4 amps, and Ohm’s law still holds.

Calculating total power What if a circuit contains more than one element? How do you calculate total power? Here are two ways: Find the power of each element separately, and add them together to get the total power. OR The next set of slides used method 2. Calculate the total power by multiplying the total current by the total voltage. 

Power for resistors in series Two 40 Ω resistors are connected in series to a 60-V battery. How much total current flows through the circuit? b) What is the power output of this circuit?

Power for resistors in parallel Two 40 Ω resistors are connected in parallel to a 60-V battery. How much total current flows through the circuit? b) What is the power output of this circuit? Point out that the TOTAL current is 3 amps. the current splits at the junction, so each resistor gets 1.5 amps.

How is your home wired? Your house is wired in parallel so each appliance will have 120 volts. Each device can be turned on and off without affecting the others. If you turn off that light bulb, you can still use the computer. Ask students to point out the advantages of the parallel arrangement: each appliance can be turned on and off independently, and each appliance gets the full 120 V. Because a house is wired in parallel, each additional appliance draws more current.

Too much current? Each additional appliance draws more current from the same outlet. If the total current exceeds the safety limit, then a circuit breaker will trip or a fuse will blow. To fix the problem: Unplug one or more appliances. Replace a blown fuse or reset the circuit breaker by flipping the switch. Point out the circuit breakers in the photo. Ask students if they have ever has to flip a circuit breaker back that was tripped. Fuses and circuit breakers limit the total current flow through the household circuits, which protects the wires from overheating and causing a fire.

Homework Two resistors with resistances of 10 Ω and 30 Ω are connected in series with a 20 volt battery. What is the equivalent resistance of the circuit? What is the current flow through the circuit? Ohm’s law works for the entire circuit.

Homework Two resistors with resistances of 10 Ω and 30 Ω are connected in parallel with a 20 volt battery. What is the equivalent resistance of the circuit? b) What is the current flow through the circuit? Notice the large current. When you add resistors in parallel, current increases.

Homework If you connect these two identical resistors as shown, will they together draw more or less current than one of the resistors alone? This question assesses the parallel combination of resistors.

Homework 4. Two 30 Ω resistors are connected in series to a 120 volt outlet. How much current flows through the circuit? b) What is the power output of this circuit?

Homework 5. Two 30 Ω resistors are connected in parallel to a 120 volt outlet. How much current flows through the circuit? b) What is the power output of this circuit?