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Voltage pushes charge, current is how much flows each second, and resistance opposes the flow; Ohm's law links them, $V = IR$.
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By the end of this lesson you will be able to find a voltage, a current or a resistance from the other two with Ohm's law.
You know that a circuit needs a complete loop from a battery through a device and back, and that switches open and close the loop. You can multiply and divide with units. This lesson puts numbers on how hard a battery pushes and how much current flows.
| Term | What it means |
|---|---|
| Current | The amount of charge flowing past a point each second, in amperes, A. |
| Voltage | The push that drives charge around a circuit, also called potential difference, in volts, V. |
| Resistance | How strongly a component opposes the flow of charge, in ohms, Ω. |
| Ohm's law | $V = IR$ for components whose resistance stays the same. |
| Coulomb | The unit of charge; one ampere is one coulomb per second. |
| Circuit breaker | A switch that opens automatically when the current is too large. |
Three quantities describe a simple circuit:
For many components they are linked by Ohm's law:
$$V = IR, \qquad I = \dfrac{V}{R}, \qquad R = \dfrac{V}{I}.$$
More voltage gives more current; more resistance gives less.
Another way: picture
Picture water flowing through a hose. The water pressure is like the voltage, the amount of water flowing each second is like the current, and a kink or a narrow nozzle is like a resistance. Turn up the pressure and more water flows; pinch the hose and less flows.
Another way: steps
Current is the flow of electric charge. In a wire, tiny charged particles called electrons drift along, and the current measures how much charge passes a point each second. One ampere means one coulomb of charge every second.
Currents in everyday devices range widely: a fraction of an ampere for a lamp or a phone, several amperes for a toaster or hair dryer, hundreds of amperes for a car's starter motor.
Voltage is the push that drives the current, the energy given to each coulomb of charge. A battery or an outlet provides it. A flashlight battery gives one and a half volts; a car battery, twelve; an American wall outlet, one hundred twenty.
Voltage is also called potential difference, because it is measured between two points, such as the two ends of a battery or the two sides of a lamp.
Resistance measures how hard it is for current to flow through something. Copper wires have very low resistance; the thin filament of an old light bulb has high resistance, which makes it glow hot.
The unit is the ohm, written with the Greek letter omega. A resistor of ten ohms lets one ampere flow when ten volts push on it.
The German scientist Georg Ohm found in 1827 that for many materials, the current is proportional to the voltage. Double the voltage and the current doubles. The ratio, voltage over current, stays the same: it is the resistance.
That gives Ohm's law, $V = IR$. It can be rearranged to find any of the three: current is voltage over resistance, and resistance is voltage over current.
A twelve-volt battery across a four-ohm resistor drives $12 \div 4 = 3$ amperes. A lamp that draws half an ampere from a hundred-twenty-volt outlet has a resistance of $120 \div 0.5 = 240$ ohms.
The units work out naturally: volts divided by ohms give amperes, and volts divided by amperes give ohms. Writing the units helps catch mistakes.
A common idea is that current gets used up as it passes through a lamp, so less comes back to the battery. In fact, the same current flows all the way around a simple loop. Every coulomb that leaves the battery comes back.
What the lamp uses is energy. Each coulomb carries energy from the battery, gives it to the lamp as light and heat, and returns to be pushed around again.
Checking an answer. Larger resistance must give smaller current for the same voltage. Multiplying the current by the resistance must give back the voltage.
Ohm's law is a result of experiment. For metal wires and ordinary resistors kept at a steady temperature, measurements show the current rising in exact proportion to the voltage, so the ratio, the resistance, is constant.
Not everything obeys it. A light bulb's resistance rises as it heats up, and some parts, like the diodes in LED bulbs, let current through only one way. For them, Ohm's law gives only a rough guide.
An ammeter measures current and is placed in the loop, so the current flows through it. A voltmeter measures voltage and is connected across a component, touching the two points on either side.
Many students use a single digital multimeter that can do both, switching between settings. Plotting voltage against current for a resistor gives a straight line whose slope is the resistance.
When current flows through a resistance, energy turns into heat. Toasters, hair dryers, space heaters and electric stoves all use this, sending large currents through wires of carefully chosen resistance so they glow hot.
The same heating is why wires are sized for the current they carry. A wire too thin for its current heats up, which is why building codes set wire sizes for each circuit.
American homes are wired with circuits protected by breakers, typically rated for fifteen or twenty amperes. If too many devices draw current at once, the total exceeds the rating and the breaker trips, opening the circuit before the wires overheat.
Plugging a space heater and a hair dryer into the same circuit can draw over twenty amperes, which is why the lights sometimes go out when both run together.
The most common error is multiplying voltage by resistance to find current, instead of dividing. Another is mixing up volts and amperes, the push and the flow.
A third is thinking current is used up. The same current flows through every part of a single loop; it is energy, not current, that the components take.
A battery turns chemical energy into electrical energy, pushing charge around a circuit. Its voltage is printed on the label: one and a half volts for AA and AAA cells, nine volts for the rectangular kind, three and seven tenths for a phone battery.
Putting batteries end to end adds their voltages. Four AA cells in a toy give six volts, pushing four times the current through the same resistance as one cell.
A few benchmarks help. An LED indicator light draws a few thousandths of an ampere. A phone charges at one to three amperes. A toaster or space heater draws about ten to fifteen. A car's starter motor, briefly, a few hundred.
An answer that says a lamp draws a thousand amperes, or a heater a thousandth, almost certainly came from dividing the wrong way.
Your body has resistance too, much of it in your dry skin, typically thousands of ohms. Wet skin has far less resistance, so the same voltage can drive a much larger, more dangerous current through you.
That is why bathrooms and kitchens in American homes use special outlets called ground-fault circuit interrupters, which cut the power in a fraction of a second if current starts leaking where it should not.
Electronic devices are full of tiny resistors, each set to a precise resistance to control the current in part of a circuit. They are marked with colored stripes that code their value in ohms.
Engineers choose resistors using Ohm's law: to let exactly the right current flow through an LED from a given voltage, they pick the resistance that makes the numbers work out.
When two lamps are connected one after the other in a single loop, called series, the current has only one path, so the same current flows through both, and their resistances add. When they are connected side by side on separate branches, called parallel, each lamp gets the full voltage of the battery.
Homes are wired in parallel, so every outlet gets the full one hundred twenty volts and each appliance can be switched on and off without affecting the others. If homes were wired in series, turning off one lamp would turn off every device in the house.
Copper has a very low resistance, so little of the battery's push is wasted in the wires and nearly all of it reaches the devices. That is why electrical cords and house wiring are made of copper, while the parts meant to get hot, like toaster coils, use metals with much higher resistance.
Wall outlets in the United States supply about one hundred twenty volts. Every appliance plugged in has a resistance, and Ohm's law sets how much current it draws. A lamp with a high resistance, a few hundred ohms, draws only half an ampere.
Heating appliances are designed with low resistance, about ten ohms, so they draw large currents, over ten amperes, and turn that into heat. Household circuits are protected by breakers rated at fifteen or twenty amperes. Running a hair dryer and a space heater on one circuit can push the total current over the limit, tripping the breaker to keep the wires from overheating. Electricians use Ohm's law to plan which outlets share a circuit.
Strings of holiday lights are popular across the country every December. Modern strings use LEDs, which need only a small current, a few hundredths of an ampere, to glow brightly.
Each LED is paired with a resistor chosen by Ohm's law, so that the voltage available drives exactly the right current. Too little resistance and the current is too large, burning out the LED; too much and the light is dim. Because LEDs draw so little current, dozens of strings can be connected end to end on one outlet without tripping a breaker, something that was impossible with older incandescent strings.
It is natural to picture a lamp using up current, so that less flows back to the battery than left it. But in a single loop, the same current flows everywhere. Measure it before and after the lamp and the ammeter reads the same.
What the lamp takes is energy: each coulomb gives up some of the energy the battery gave it, turning it into light and heat. The charge itself keeps circulating around the loop.
A flashlight runs on two $1.5$ V batteries in a row. Find the total voltage.
$V = 1.5 + 1.5 = 3\ \text{V}$
Voltages add in a row.
The bulb's resistance is $6$ Ω. Write Ohm's law for the current.
$I = \dfrac{V}{R}$
Push over opposition.
Find the current.
$I = \dfrac{3}{6} = 0.5\ \text{A}$
Half an ampere.
Find the current with one battery.
$I = \dfrac{1.5}{6} = 0.25\ \text{A}$
Half the voltage.
Describe the bulb then.
$\text{dimmer}$
Less current.
A space heater plugged into a $120$ V outlet draws $12$ A. Write Ohm's law for resistance.
$R = \dfrac{V}{I}$
Voltage over current.
Substitute the values.
$R = \dfrac{120}{12}$
Volts over amperes.
Evaluate the resistance.
$R = 10\ \Omega$
Ohms.
A lamp on the same outlet draws $0.5$ A. Find its resistance.
$R = \dfrac{120}{0.5} = 240\ \Omega$
Much higher.
Compare the two devices.
$\text{low resistance, big current}$
The heater draws more.
Check the heater with Ohm's law.
$12 \times 10 = 120\ \text{V}$
Matches the outlet.
A $9$ V battery drives current through a $3$ Ω resistor. Find the current.
$I = \dfrac{9}{3} = 3\ \text{A}$
Ohm's law.
Replace it with a $9$ Ω resistor. Find the current.
$I = \dfrac{9}{9} = 1\ \text{A}$
Three times the resistance.
Describe the change.
$\text{a third of the current}$
Inverse proportion.
Keep $9$ Ω and use $18$ V. Find the current.
$I = \dfrac{18}{9} = 2\ \text{A}$
Twice the voltage.
Find the charge in one minute at $2$ A.
$Q = 2 \times 60 = 120\ \text{C}$
Current times time.
Find the resistance for $0.5$ A from $18$ V.
$R = \dfrac{18}{0.5} = 36\ \Omega$
Voltage over current.
Check the answer.
$0.5 \times 36 = 18\ \text{V}$
Gives back the voltage.
Write Ohm's law for the current.
$I = \dfrac{V}{R}$
Push over opposition.
Substitute the values.
$I = \dfrac{6}{3}$
Volts over ohms.
Evaluate the current.
A $9$ V battery is connected across a $6$ Ω resistor. What current flows, in A?
Complete the worked solution: a $12$ V supply drives current through a $3$ Ω resistor. Find the current in A, the current in A if the resistance is doubled, and the charge in coulombs that passes through the original resistor in $10$ s.
Find the current.
$I = \dfrac{V}{R} =$ a
Ohm's law.
Find the current with double resistance.
$I_2 = \dfrac{V}{2R} =$ b
Half the current.
Find the charge in ten seconds.
$Q = I \times 10 =$ q
Current times time.
Note where the charge goes.
$\text{around the loop and back}$
It is not used up.
Match each circuit word to its meaning.
| the charge flowing each second, in amperes | the push that drives charge around, in volts | how strongly a component opposes the flow, in ohms | voltage equals current times resistance | |
|---|---|---|---|---|
| current | ||||
| voltage | ||||
| resistance | ||||
| Ohm's law |
A $10$ Ω resistor is connected to a $5$ V supply. Fill in the current in A, the current in A if the voltage is doubled, and the resistance in Ω that would halve the original current.
| value | |
|---|---|
| current (A) | |
| current at twice the voltage (A) | |
| resistance that halves the current (Ω) |
In a lab, different currents are sent through a $100$ Ω resistor. Write the voltage across it, in V, as a function of the current $I$ in amperes.
Answer:
a desk lamp runs on $120$ V and draws a current of $0.5$ A. What is its resistance, in Ω?
Answer: Ω
Household outlets in the United States supply $120$ V. When running, a hair dryer has a resistance of about $9.6$ Ω. What current does it draw, in A?
Answer: A
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
In a lab, different currents are sent through a $12$ Ω resistor. Write the voltage across it, in V, as a function of the current $I$ in amperes.
Answer:
You can use Ohm's law. Explain to someone why a space heater draws much more current than a lamp from the same outlet.
29. Your turn: a $6$ V battery is connected across a $3$ Ω resistor. What current flows?, step 3
$I = 2\ \text{A}$
Amperes.