Download electricity practice problems

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Ohm's Law
13.3
A German physicist, Georg S. Ohm, developed this mathematical relationship, which is present in most circuits.
This relationship is known as Ohm's law. This relationship states that if the voltage (energy) in a circuit increases,
so does the current (flow of charges). If the resistance increases, the current flow decreases.
Voltage (volts)
Current (amps) = ---------------------------------------------Resistance (ohms, : )
To work through this skill sheet, you will need the symbols used to depict circuits in
diagrams. The symbols that are most commonly used for circuit diagrams are
provided to the right.
If a circuit contains more than one battery, the total voltage is the sum of the
individual voltages. A circuit containing two 6 V batteries has a total voltage of 12 V.
[Note: The batteries must be connected positive to negative for the voltages to add.]
If a toaster produces 12 ohms of resistance in a 120-volt circuit, what is the amount of
current in the circuit?
Given
The resistance (R) is 12 ohms.
The voltage (V) is 120 volts.
Looking for
The amount of current (I) in the circuit.
Relationships
V
I = --R
Solution
volts- = 10 amps
I = V
--- = 120
--------------------R
12 ohms
The current in the toaster circuit is 10 amps.
If a problem asks you to calculate the voltage or resistance, you must rearrange the equation I=V/R to solve for V
or R. All three forms of the equation are listed below.
V
II = VV
--V IR
R
R
R
I
In this section, you will find some problems based on diagrams and others without diagrams. In all cases, show
your work.
1.
How much current is in a circuit that includes a 9-volt battery and a bulb with a resistance of 3 ohms?
2.
How much current is in a circuit that includes a 9-volt battery and a bulb with a resistance of 12 ohms?
3.
A circuit contains a 1.5 volt battery and a bulb with a resistance of 3 ohms. Calculate the current.
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4.
A circuit contains two 1.5 volt batteries and a bulb with a resistance of 3 ohms. Calculate the current.
5.
What is the voltage of a circuit with 15 amps of current and toaster with 8 ohms of resistance?
6.
A light bulb has a resistance of 4 ohms and a current of 2 A. What is the voltage across the bulb?
7.
How much voltage would be necessary to generate 10 amps of current in a circuit that has 5 ohms of
resistance?
8.
How many ohms of resistance must be present in a circuit that has 120 volts and a current of 10 amps?
9.
An alarm clock draws 0.5 A of current when connected to a 120 volt circuit. Calculate its resistance.
13.3
10. A portable CD player uses two 1.5 V batteries. If the current in the CD player is 2 A, what is its resistance?
11. You have a large flashlight that takes 4 D-cell batteries. If the current in the flashlight is 2 amps, what is the
resistance of the light bulb? (Hint: A D-cell battery has 1.5 volts.)
12. Use the diagram below to answer the following problems.
a.
What is the total voltage in each circuit?
b.
How much current would be measured in each circuit if the light bulb has a resistance of 6 ohms?
c.
How much current would be measured in each circuit if the light bulb has a resistance of 12 ohms?
d.
Is the bulb brighter in circuit A or circuit B? Why?
13. What happens to the current in a circuit if a 1.5-volt battery is removed and is replaced by a 9-volt battery?
14. In your own words, state the relationship between resistance and current in a circuit.
15. In your own words, state the relationship between voltage and current in a circuit.
16. What could you do to a closed circuit consisting of 2 batteries, 2 light bulbs, and a switch to increase the
current? Explain your answer.
17. What could you do to a closed circuit consisting of 2 batteries, 2 light bulbs, and a switch to decrease the
current? Explain your answer.
18. You have four 1.5 V batteries, a 1: bulb, a 2: bulb, and a 3: bulb. Draw a circuit you could build to
create each of the following currents. There may be more than one possible answer for each.
a.
1 ampere
b.
2 amperes
c.
3 amperes
d.
6 amperes
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Series Circuits
14.1
In a series circuit, current follows only one path from the positive end of the battery toward the negative end. The
total resistance of a series circuit is equal to the sum of the individual resistances. The amount of energy used by
a series circuit must equal the energy supplied by the battery. In this way, electrical circuits follow the law of
conservation of energy. Understanding these facts will help you solve problems that deal with series circuits.
To answer the questions in the practice section, you will have to use Ohm's law. Remember that:
Voltage (volts)
Current (amps) = --------------------------------------Resistance (ohms)
Some questions ask you to calculate a voltage drop. We often say that each resistor (or light bulb) creates a
separate voltage drop. As current flows along a series circuit, each resistor uses up some energy. As a result, the
voltage gets lower after each resistor. If you know the current in the circuit and the resistance of a particular
resistor, you can calculate the voltage drop using Ohm’s law.
Voltage drop across resistor (volts) = Current through resistor (amps) u Resistance of one resistor (ohms)
1.
2.
Use the series circuit pictured to the right to answer
questions (a)-(e).
a.
What is the total voltage across the bulbs?
b.
What is the total resistance of the circuit?
c.
What is the current in the circuit?
d.
What is the voltage drop across each light bulb?
(Remember that voltage drop is calculated by
multiplying current in the circuit by the resistance of a
particular resistor: V = IR.)
e.
Draw the path of the current on the diagram.
Use the series circuit pictured to the right to answer
questions (a)-(e).
a.
What is the total voltage across the bulbs?
b.
What is the total resistance of the circuit?
c.
What is the current in the circuit?
d.
What is the voltage drop across each light bulb?
e.
Draw the path of the current on the diagram.
3.
What happens to the current in a series circuit as more light bulbs are added? Why?
4.
What happens to the brightness of each bulb in a series circuit as additional bulbs are added? Why?
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5.
6.
7.
8.
9.
Use the series circuit pictured to the right to answer
questions (a), (b), and (c).
a.
What is the total resistance of the circuit?
b.
What is the current in the circuit?
c.
What is the voltage drop across each resistor?
Use the series circuit pictured to the right to answer
questions (a)-(e).
a.
What is the total voltage of the circuit?
b.
What is the total resistance of the circuit?
c.
What is the current in the circuit?
d.
What is the voltage drop across each light bulb?
e.
Draw the path of the current on the diagram.
Use the series circuit pictured right to answer questions
(a), (b), and (c). Consider each resistor equal to all others.
a.
What is the resistance of each resistor?
b.
What is the voltage drop across each resistor?
c.
On the diagram, show the amount of voltage in the
circuit before and after each resistor.
Use the series circuit pictured right to answer questions (a) (d).
a.
What is the total resistance of the circuit?
b.
What is the current in the circuit?
c.
What is the voltage drop across each resistor?
d.
What is the sum of the voltage drops across the three
resistors? What do you notice about this sum?
Use the diagram to the right to answer
questions (a), (b), and (c).
a.
How much current would be measured
in each circuit if each light bulb has a
resistance of 6 ohms?
b.
How much current would be measured
in each circuit if each light bulb has a
resistance of 12 ohms?
c.
What happens to the amount of current
in a series circuit as the number of
batteries increases?
14.1
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Parallel Circuits
14.2
A parallel circuit has at least one point where the circuit divides, creating more than one path for current. Each
path is called a branch. The current through a branch is called branch current. If current flows into a branch in a
circuit, the same amount of current must flow out again, This rule is known as Kirchoff’s current law.
Because each branch in a parallel circuit has its own path to the battery, the voltage across each branch is equal to
the battery’s voltage. If you know the resistance and voltage of a branch you can calculate the current with Ohm’s
Law (I=V/R).
1.
2.
3.
4.
Use the parallel circuit pictured right to answer
questions (a) - (d).
a.
What is the voltage across each bulb?
b.
What is the current in each branch?
c.
What is the total current provided by the battery?
d.
Use the total current and the total voltage to
calculate the total resistance of the circuit.
Use the parallel circuit pictured right to answer
questions (a) - (d).
a.
What is the voltage across each bulb?
b.
What is the current in each branch?
c.
What is the total current provided by the battery?
d.
Use the total current and the total voltage to
calculate the total resistance of the circuit.
Use the parallel circuit pictured right to answer
questions (a) - (d).
a.
What is the voltage across each resistor?
b.
What is the current in each branch?
c.
What is the total current provided by the
batteries?
d.
Use the total current and the total voltage to calculate the total resistance of the circuit.
Use the parallel circuit pictured right to answer
questions (a) - (c).
a.
What is the voltage across each resistor?
b.
What is the current in each branch?
c.
What is the total current provided by the
battery?
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14.2
In part (d) of problems 1, 2, and 3, you calculated the total resistance of each circuit. This required you to first
find the current in each branch. Then you found the total current and used Ohm’s law to calculate the total
resistance. Another way to find the total resistance of two parallel resistors is to use the formula shown below.
R to ta l
R1 u R 2
R1 R 2
Calculate the total resistance of a circuit containing two 6 ohm resistors.
Given
The circuit contains two 6 : resistors in parallel.
Looking for
The total resistance of the circuit.
Relationships
R to ta l
1.
2.
Solution
R to ta l
R to ta l
6:u6:
6: 6:
3:
The total resistance is 3 ohms.
R1 u R 2
R1 R 2
Calculate the total resistance of a circuit containing each of the following combinations of resistors.
a.
Two 8 : resistors in parallel
b.
Two 12 : resistors in parallel
c.
A 4 : resistor and an 8 : resistor in parallel
d.
A 12 : resistor and a 3 : resistor in parallel
To find the total resistance of three resistors A, B, and C in parallel, first use the formula to find the total of
resistors A and B. Then use the formula again to combine resistor C with the total of A and B. Use this
method to find the total resistance of a circuit containing each of the following combinations of resistors
a.
Three 8 : resistors in parallel
b.
Two 6 : resistors and a 2 : resistor in parallel
c.
A 1 :, a 2 :, and a 3 : resistor in parallel
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Electrical Power
14.3
How do you calculate electrical power?
In this skill sheet you will review the relationship between electrical power and Ohm’s law. As you work through
the problems, you will practice calculating the power used by common appliances in your home.
During everyday life we hear the word watt mentioned in reference to things like light bulbs and electric bills.
The watt is the unit that describes the rate at which energy is used by an electrical device. Energy is never created
or destroyed, so “used” means it is converted from electrical energy into another form such as light or heat. And
since energy is measured in joules, power is measured in joules per second. One joule per second is equal to one
watt.
We can calculate the amount of electrical power by an appliance or other electrical component by multiplying the
voltage by the current.
Current x Voltage = Power, or P = IV
A kilowatt (kWh) is 1,000 watts or 1,000 joules of energy per second. On an electric bill you may have noticed
the term kilowatt-hour. A kilowatt-hour means that one kilowatt of power has been used for one hour. To
determine the kilowatt-hours of electricity used, multiply the number of kilowatts by the time in hours.
.
You use a 1500 watt hair heater for 3 hours. How many kilowatt-hours of electricity did you use?
Given
The power of the heater is 1500 watts.
The heater was used for 3 hours.
Looking for
The number of kilowatt-hours.
Relationships
kilowatt-hours = kilowatts x hours
1.
2.
Solution
1500 watts u
1 kilowatt
1.5 kilowatts
1000 watts
1.5 kilowatts u 3 hours = 4.5 kilowatt-hours
You used 4.5 kilowatt-hours of electricity.
Your oven has a power rating of 5000 watts.
a.
How many kilowatts is this?
b.
If the oven is used for 2 hours to bake cookies, how many kilowatt-hours (kWh) are used?
c.
If your town charges $0.15/kWh, what is the cost to use the oven to bake the cookies?
You use a 1200-watt hair dryer for 10 minutes each day.
a.
How many minutes do you use the hair dryer in a month? (Assume there are 30 days in the month.)
b.
How many hours do you use the hair dryer in a month?
c.
What is the power of the hair dryer in kilowatts?
d.
How many kilowatt-hours of electricity does the hair dryer use in a month?
e.
If your town charges $0.15/kWh, what is the cost to use the hair dryer for a month?
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3.
Calculate the power rating of a home appliance (in kilowatts) that uses 8 amps of current when
plugged into a 120-volt outlet.
4.
Calculate the power of a motor that draws a current of 2 A when connected to a 12 volt battery.
5.
Your alarm clock is connected to a 120 volt circuit and draws 0.5 A of current.
14.3
a.
Calculate the power of the alarm clock in watts.
b.
Convert the power to kilowatts.
c.
Calculate the number of kilowatt-hours of electricity used by the alarm clock if it is left on for one year.
d.
Calculate the cost of using the alarm clock for one year if your town charges $0.15/kWh.
6.
Using the formula for power, calculate the amount of current through a 75-watt light bulb that is connected
to a 120-volt circuit in your home.
7.
The following questions refer to the diagram.
a. What is the total voltage of the circuit?
b. What is the current in the circuit?
c. What is the power of the light bulb?
8.
9.
A toaster is plugged into a 120-volt household circuit. It draws 5 amps of
current.
a.
What is the resistance of the toaster?
b.
What is the power of the toaster in watts?
c.
What is the power in kilowatts?
A clothes dryer in a home has a power of 4,500 watts and runs on a special 220-volt household circuit.
a.
What is the current through the dryer?
b.
What is the resistance of the dryer?
c.
How many kilowatt-hours of electricity are used by the dryer if it is used for 4 hours in one week?
d.
How much does it cost to run the dryer for one year if it is used for 4 hours each week at a cost of
$0.15/kWh?
10. A circuit contains a 12-volt battery and two 3-ohm bulbs in series.
a.
Calculate the total resistance of the circuit.
b.
Calculate the current in the circuit.
c.
Calculate the power of each bulb.
d.
Calculate the power supplied by the battery.
11. A circuit contains a 12-volt battery and two 3-ohm bulbs in parallel.
a.
What is the voltage across each branch?
b.
Calculate the current in each branch.
c.
Calculate the power of each bulb.
d.
Calculate the total current in the circuit.
e.
Calculate the power supplied by the battery.
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Date:
Coulomb’s Law
15.2
In this skill sheet, you will work with Coulomb’s law. There are many similarities and some differences between
the equation of universal gravitation and the equation for Coulomb’s law. They are both inverse square law
relationships, and they both have similar arrangements of variables.
When two charges q1 and q2 are separated by a distance r, there exists a force between them that is given by:
where F equals the force in newtons and K is a constant equal to 9 u 109 N-m2/C2. The units of q1 and q2 are the
coulombs (C). Distance is given in meters. Here are some important points about the relationships of the
variables in Coulomb’s law.
•
Force is inversely proportional to the square of the distance between the charges. Therefore, if the distance
increases by a factor of 2, the force decreases by a factor of 4.
•
Force is proportional to the strength of each charge.
•
When the two charges have the same sign (positive or negative), the force between them is repulsive because
like charges repel.
•
When the charges have opposite signs, the force between them is attractive because unlike charges attract.
1.
What happens to the force between two charges if the distance between them is tripled?
2.
What happens to the force between two charges if the distance between them is quadrupled?
3.
What happens to the force between two charges if the distance between them is cut in half?
4.
What happens to the force between two charges if the magnitude of one charge is doubled?
5.
What happens to the force between two charges is the magnitude of both charges is doubled?
6.
What happens to the force between two charges if the magnitude of both charges is doubled and the distance
between them is doubled?
7.
What happens to the force between two charges if the magnitude of both charges is doubled and the distance
between them is cut in half?
Page 2 of 2
15.2
The example below shows how to use Coulomb’s law to calculate the strength of the force between two charges.
A 0.001 coulomb charge and a 0.002 coulomb charge are 2 meters apart. Calculate the force between them.
Given
The charges have magnitudes of 0.003 C and
0.005 C.
The charges are 2 meters apart.
Looking for
The force between the charges.
Solution
V
F
2- 2
(9 u 109 IN =
<m-R/C )
F
4500 N
(0.001 C)(0.002 C)
(2 m) 2
The force is 4500 newtons.
Relationships
V q q
FI = --Rk- 1 2 2
r
1.
Two particles, each with a charge of 1 C, are separated by a distance of 1 meter. What is the force between
the particles?
2.
What is the force between a 3 C charge and a 2 C charge separated by a distance of 5 meters?
3.
Calculate the force between a 0.006 C charge and a 0.001 C charge 4 meters apart.
4.
Calculate the force between a 0.05 C charge and a 0.03 C charge 2 meters apart.
5.
Two particles are each given a charge of 5 u 10-5 C. What is the force between the charged particles if the
distance between them is 2 meters?
6.
The force between a pair of charges is 100 newtons. The distance between the charges is 0.01 meter. If one
of the charges is 2 u 10-10 C, what is the strength of the other charge?
7.
Two equal charges separated by a distance of 1 meter experience a repulsive force of 1,000 newtons. What is
the strength in coulombs of each charge?
8.
The force between a pair of 0.001 C charges is 200 N. What is the distance between them?
9.
The force between two charges is 1000 N. One has a charge of 2 u 10-5 C, and the other has a charge of
5 u 10-6 C. What is the distance between them?
10. The force between two charges is 2 newtons. The distance between the charges is 2 u 10-4 m. If one of the
charges is 3 u 10-6 C, what is the strength of the other charge?