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Electricity & Magnetism Unit

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Understanding Circuits

- Recognize and sketch examples of series and parallel circuits.
- Describe a short circuit and why a short circuit may be a dangerous hazard.
- Calculate the current in a series or parallel circuit containing up to three resistances.
- Calculate the total resistance of a circuit by combining series or parallel resistances.
- Describe the differences between AC and DC electricity.
- Calculate the power used in an AC or DC circuit from the current and voltage.

- series circuit
- parallel circuit
- short circuit
- network circuit
- circuit analysis
- power
- Kirchhoff’s voltage law
- voltage drop direct
- current (DC)

- alternating current (AC)
- kilowatt
- Kirchhoff’s current law
- horsepower
- power factor
- circuit breaker
- watt
- kilowatt-hour

Key Question:

How do series and parallel circuits work?

*Students read Section 20.1 AFTER Investigation 20.1

- In series circuits, current can only take one path.
- The amount of current is the same at all points in a series circuit.

- Each resistance in a series circuit adds to the total resistance of the circuit.

Rtotal = R1 + R2 + R3...

Total resistance

(ohms)

Individual resistances (W)

- Light bulbs, resistors, motors, and heaters usually have much greater resistance than wires and batteries.

- How much current flows in a circuit with a 1.5-volt battery and three 1 ohm resistances (bulbs) in series?

- Each separate resistance creates a voltage drop as the current passes through.
- As current flows along a series circuit, each type of resistor transforms some of the electrical energy into another form of energy
- Ohm’s law is used to calculate the voltage drop across each resistor.

- In parallel circuits the current can take more than one path.
- Because there are multiple branches, the current is not the same at all points in a parallel circuit.

- Sometimes these paths are called branches.
- The current through a branch is also called the branch current.
- When analyzing a parallel circuit, remember that the current always has to go somewhere.
- The total current in the circuit is the sum of the currents in all the branches.
- At every branch point the current flowing out must equal the current flowing in.
- This rule is known as Kirchhoff’s current law.

- In a parallel circuit the voltageis the same across each branch because each branch has a low resistance path back to the battery.
- The amount of current in each branch in a parallel circuit is notnecessarily the same.
- The resistance in each branch determines the current in that branch.

Parallel circuits have two big advantages over series circuits:

1. Each device in the circuit sees the full battery voltage.

2. Each device in the circuit may be turned off independently without stopping the current flowing to other devices in the circuit.

- A short circuit is a parallel path in a circuit with zero or very low resistance.
- Short circuits can be made accidentally by connecting a wire between two other wires at different voltages.
- Short circuits are dangerous because they can draw huge amounts of current.

- Two bulbs with different resistances are connected in parallel to batteries with a total voltage of 3 volts.
- Calculate the total current supplied by the battery.

- Adding resistance in parallel provides another path for current, and more current flows.
- When more current flows for the same voltage, the total resistance of the circuit decreases.
- This happens because every new path in a parallel circuit allows more current to flow for the same voltage.

- A circuit contains a 2 ohm resistor and a 4 ohm resistor in parallel.
- Calculate the total resistance of the circuit.

- Identify what the problem is asking you to find. Assign variables to the unknown quantities.
- Make a large clear diagram of the circuit. Label all of the known resistances, currents, and voltages. Use the variables you defined to label the unknowns.
- You may need to combine resistances to find the total circuit resistance. Use multiple steps to combine series and parallel resistors.

- If you know the total resistance and current, use Ohm’s law as V = IR to calculate voltages or voltage drops. If you know the resistance and voltage, use Ohm’s law as I = V ÷ R to calculate the current.
- An unknown resistance can be found using Ohm’s law as R = V ÷ I, if you know the current and the voltage drop through the resistor.
- Use Kirchhoff’scurrent and voltage laws as necessary.

- A bulb with a resistance of 1Ω is to be used in a circuit with a 6-volt battery.
- The bulb requires 1 amp of current.
- If the bulb were connected directly to the battery, it would draw 6 amps and burn out instantly.
- To limit the current, a resistor is added in series with the bulb.
- What size resistor is needed to make the current 1 amp?

- In many circuits, resistors are connected both in series and in parallel.
- Such a circuit is called a network circuit.
- There is no single formula for adding resistors in a network circuit.
- For very complex circuits, electrical engineers use computer programs that can rapidly solve equations for the circuit using Kirchhoff’s laws.

- Three bulbs, each with a resistance of 3Ω, are combined in the circuit in the diagram
- Three volts are applied to the circuit.
- Calculate the current in each of the bulbs.
- From your calculations, do you think all three bulbs will be equally bright?

- The watt (W) is a unit of power.
- Power is the rate at which energy moves or is used.
- Since energy is measured in joules, power is measured in joules per second.
- One joule per second is equal to one watt.

- One watt is a pretty small amount of power.
- In everyday use, larger units are more convenient to use.
- A kilowatt (kW) is equal to 1,000 watts.
- The other common unit of power often seen on electric motors is the horsepower.
- One horsepower is 746 watts.

Voltage (volts)

P = VI

Current (amps)

Power (watts)

- A light bulb with a resistance of 1.5Ω is connected to a 1.5-volt battery in the circuit shown at right.
- Calculate the power used by the light bulb.

- Electric companies charge for the number of kilowatt-hours used during a set period of time, often a month.
- One kilowatt-hour (kWh) means that a kilowatt of power has been used for one hour.
- Since power multiplied by time is energy, a kilowatt-hour is a unit of energy.
- One kilowatt-hour is 3.6 x 106 joules.

- Your electric company charges 14 cents per kilowatt-hour. Your coffee maker has a power rating of 1,050 watts.
- How much does it cost to use the coffee maker one hour per day for a month?

- The current from a battery is always in the same direction.
- One end of the battery is positive and the other end is negative.
- The direction of current flows from positive to negative.
- This is called direct current, or DC.

- If voltage alternates, so does current.
- When the voltage is positive, the current in the circuit is clockwise.
- When the voltage is negative the current is the opposite direction.
- This type of current is called alternating current, or AC.

- AC current is used for almost all high-power applications because it is easier to generate and to transmit over long distances.
- The 120 volt AC (VAC) electricity used in homes and businesses alternates between peak values of +170 V and -170 V at a frequency of 60 Hz.
- AC electricity is usually identified by the average voltage, (120 VAC) not the peak voltage.

- For a circuit containing a motor, the power calculation is a little different from that for a simple resistance like a light bulb.
- Because motors store energy and act like generators, the current and voltage are not in phase with each other.
- The current is always a little behind the voltage.

- Electrical engineers use a power factor (pf) to calculate power for AC circuits with motors

Avg. voltage

(volts)

Avg. current (amps)

P = VI x pf

Power (watts)

power factor

0-100%