cp35 Precalculus with Limits CHapter 5 answers

A Battery and a BulbA Battery and a Bulb

• The most important thing is that there must be a complete path, or circuit, from the positive terminal at the top of the battery to the negative terminal.

• The most important thing is that there must be a complete path, or circuit, from the positive terminal at the top of the battery to the negative terminal.

A Battery and a BulbA Battery and a Bulb• Although current flows

from the positive terminal to the negative, the electrons actually flow from the negative terminal to the base of the bulb, THROUGH the filament, back to the base of the bulb, and finally to the positive terminal.

• Although current flows from the positive terminal to the negative, the electrons actually flow from the negative terminal to the base of the bulb, THROUGH the filament, back to the base of the bulb, and finally to the positive terminal.


• The flow of electric current is similar to the flow of water. The battery acts as a pump which produces the change in pressure that causes the current to flow.

• The flow of electric current is similar to the flow of water. The battery acts as a pump which produces the change in pressure that causes the current to flow.


• If the batteries in a circuit are connected in series, (positive of first battery to the negative of the next, the voltage across the bulb is the SUM of all the individual voltages added together.

• If the batteries in a circuit are connected in series, (positive of first battery to the negative of the next, the voltage across the bulb is the SUM of all the individual voltages added together.

Electric CircuitsElectric Circuits

• For the continual flow of electrons there MUST be a complete circuit with NO gaps. Unlike a water faucet which needs to be open for water to flow, CLOSING a switch causes the current to flow.

• For the continual flow of electrons there MUST be a complete circuit with NO gaps. Unlike a water faucet which needs to be open for water to flow, CLOSING a switch causes the current to flow.

Series CircuitsSeries Circuits

• In a series circuit the current has only ONE path. This means the current through each electrical device is the same.

• In a series circuit the current has only ONE path. This means the current through each electrical device is the same.

Series CircuitsSeries Circuits• The current is

slowed (resisted) by the first, then the second, then the third bulb. The total resistance is the sum of the individual resistances along the circuit path.

• The current is slowed (resisted) by the first, then the second, then the third bulb. The total resistance is the sum of the individual resistances along the circuit path.

Series CircuitsSeries Circuits• The current in the

circuit is numerically equal to the voltage supplied divided by the total resistance. In this case the current (I = V/R) is 9/22 or .41 Amps.

• The current in the circuit is numerically equal to the voltage supplied divided by the total resistance. In this case the current (I = V/R) is 9/22 or .41 Amps.

Series CircuitsSeries Circuits• The Voltage drop across

EACH device depends on the resistance according to Ohms Law (V=IR)

• .41 * 2 = .82 volts• .41 * 8 = 3.28 volts• .41 * 12 = 4.92 volts• The total voltage drop

around the circuit will equal the voltage drop across the battery.

• The Voltage drop across EACH device depends on the resistance according to Ohms Law (V=IR)

• .41 * 2 = .82 volts• .41 * 8 = 3.28 volts• .41 * 12 = 4.92 volts• The total voltage drop

around the circuit will equal the voltage drop across the battery.

Parallel CircuitsParallel Circuits• A Parallel circuit is

where the flow of electrons can take two or more paths instead of following only a single path as in a series circuit.

• A Parallel circuit is where the flow of electrons can take two or more paths instead of following only a single path as in a series circuit.

Parallel CircuitsParallel Circuits• In this simple

parallel circuit each of the lamps has it’s own branch from the main current flow. Since all the bulbs have the same resistance, they each get 1/3 of the current.

• In this simple parallel circuit each of the lamps has it’s own branch from the main current flow. Since all the bulbs have the same resistance, they each get 1/3 of the current.

The total current is the sum of the currents in each of the branches.

Parallel CircuitsParallel Circuits

• The total resistance in a group of parallel resisters can be calculated with the equation at the right.

• The total resistance in a group of parallel resisters can be calculated with the equation at the right.

Schematic DiagramsSchematic Diagrams

• Electric circuits are frequently described by simple diagrams called schematic diagrams.

• Electric circuits are frequently described by simple diagrams called schematic diagrams.

Review

Series Circuits1.Current is constant and depends on total resistance2.Voltage drop on each resistor is dependent on total current and is adititve in the circuit.3.Total resistance is summative.

Parallel Circuits1.Voltage is constant2.Current is Adititve and is dependent on the resistance in each branch.3.Resistance is the reciprocal of the sum of the reciprocal resistances

Resistors in Compound Circuit


• It is possible to determine the equivalent resistance equivalent resistance of a group of resistors that are in a parallel branch.

• The two parallel resistors R3 (6) and R4

(2) give an equivalent resistance of 1.5 ohms.

• It is possible to determine the equivalent resistance equivalent resistance of a group of resistors that are in a parallel branch.

• The two parallel resistors R3 (6) and R4

(2) give an equivalent resistance of 1.5 ohms.



• The 1.5 ohms can be substituted for the two resistors in the circuit. This value is in series with the 2.5 ohms of R5

so they can be added together to equal 4.0 ohms. This would then be parallel with another 4.0 ohms.

• The 1.5 ohms can be substituted for the two resistors in the circuit. This value is in series with the 2.5 ohms of R5

so they can be added together to equal 4.0 ohms. This would then be parallel with another 4.0 ohms.

• These two parallel 4 ohm resistors are equivalent to one 2 ohm resistance.

• These two parallel 4 ohm resistors are equivalent to one 2 ohm resistance.



• This 2 ohm resistor is now in series with the last 6 ohm resistor. This give a total of 8 ohms in the entire circuit.

• This 2 ohm resistor is now in series with the last 6 ohm resistor. This give a total of 8 ohms in the entire circuit.



• This gives a total resistance of 8 ohms. If the battery was 24 volts, then the current (I) would be 24/8 or 3.0 amps

• This gives a total resistance of 8 ohms. If the battery was 24 volts, then the current (I) would be 24/8 or 3.0 amps



Parallel Circuits and Overloading


• There are two power lines that come into your home. One is +120 volts and the other is -120 volts. Connecting these two together produces 240 volts for larger appliances. Connecting +120 volt line to the ground gives 120 volts for regular appliances.

• There are two power lines that come into your home. One is +120 volts and the other is -120 volts. Connecting these two together produces 240 volts for larger appliances. Connecting +120 volt line to the ground gives 120 volts for regular appliances.



• Since household circuits are wired in parallel the current increases as each appliance is turned on. The hair dryer draws 10A and the stereo draws 3A. But if you add the heater at 13A the total is more than the circuit can safely handle.

• Too large a current will heat the wires to the point where they could start a fire in the walls.

• Since household circuits are wired in parallel the current increases as each appliance is turned on. The hair dryer draws 10A and the stereo draws 3A. But if you add the heater at 13A the total is more than the circuit can safely handle.

• Too large a current will heat the wires to the point where they could start a fire in the walls.



• To prevent overloading in circuits fuses were used in series with the power lines. A soft metal was used which would melt and break the circuit if too much current was used.

• To prevent overloading in circuits fuses were used in series with the power lines. A soft metal was used which would melt and break the circuit if too much current was used.



• Today, most circuits are protected by circuit breakers which snap off if too much current goes through. These are better than fuses because they do not have to be replaced each time.

• Today, most circuits are protected by circuit breakers which snap off if too much current goes through. These are better than fuses because they do not have to be replaced each time.

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cp35 Precalculus with Limits CHapter 5 answers