The flight crew reports a dim landing light. You install a new lamp and check that the circuit breaker has not opened. With the light on, you measure 28 V at the bus but only 22.3 V across the lamp.
FIG 1 The landing light circuit.
28 V
At the bus
Measured at the bus with the light on.
22.3 V
Across the lamp
Measured across the new lamp. It is 5.7 V less than the bus.
The lamp shares one path with the circuit breaker, the switch, a connector, the wiring and the ground, so the other 5.7 V is being dropped across one of those parts. This lesson shows you how to find which part, by knowing what each part should drop.
Bus
A metal bar that is the common point where electrical power is shared out to the circuits. The circuit breakers take their power from it.
Circuit breaker
A switch that opens by itself when the current is too high, to protect the wire. A fuse does the same job by melting open, and it must be replaced. A circuit breaker can be reset by hand, but only after the fault that tripped it has been found and fixed.
Learning Objectives
When you finish this lesson you can do the four things below. The check at the end asks about each of them.
1IdentifyIdentify a series circuit by tracing its one path, and use the rule that the current is the same at every point in it.
2CalculateCalculate the total resistance and the total current of a series circuit.
3CalculateCalculate the voltage drop across each part, and confirm that the drops add up to the source voltage.
4PredictPredict what a break in the path (an open), or added resistance, does to the current and to every voltage drop in the circuit.
Key Facts
One path
The same current flows through every part of the circuit.
Total resistance
Add the resistances to get the total, then divide the source voltage by the total to get the current.
Voltage drops
Each drop is the current times that part's resistance, and the drops add up to the source voltage.
Opens and added resistance
A break in the path, called an open, stops the current everywhere. Added resistance lowers the current and changes every drop.
Lecture Video
Watch the lecture. Continue appears when it ends. You can skip it for now and reopen it from this page later. The lecture is 5:18 long.
Current Through One Load
In the Ohm's Law lesson, you worked with one load, the part that does the work, on one source. This lesson uses the same law on circuits with more than one load. The question below uses a single load.
FIG 2 One load: a 20 ohm resistor across a 9 V source.
E = I × R I = E / R R = E / I
Quick recall
A 9 V source is connected across a single 20 ohm load. What current flows?
Identifying a Series Circuit
Series circuits have only one path for current to flow. Start at the source, trace through each part in turn, and you come back to the source without reaching a branch, a point where the path splits into two or more paths.
Series circuit
A circuit with only one path for current. The parts are connected end to end, so the same current flows through each one.
FIG 3 A 12 V source with two resistors, R1 (10 ohms) and R2 (30 ohms), connected end to end. Source: FAA-H-8083-30B, Figure 12-82.
The path goes from the source, through R1, through R2 and back to the source. There is one path and no branch, so this is a series circuit.
Check your understanding
Which drawing shows a series circuit?
Current in a Series Circuit
There is only one path, so every electron that leaves the source passes through every part on its way back. The current is the same at every point in a series circuit.
It = I1 = I2 = In
Total current (It) equals the current through the first part (I1), which equals the current through the second part (I2), and so on for every part.
It?
I1?
I2?
I3?
All four ammeters read 0.50 A. The current is the same at every point.
FIG 4 Four ammeters at four points around one series loop. Select each ammeter to see its reading.
Current Through a Load
A lamp changes electrical energy into light and heat. The electrons pass through it and continue around the loop, so an ammeter after the lamp reads the same current as one before it.
Check your understanding
A 28 V bus feeds a lamp through a circuit breaker, a switch and a wire. An ammeter between the circuit breaker and the switch reads 2.4 A. What does an ammeter in the return wire, after the lamp, read?
Ammeter Readings That DifferIf two ammeters on one path read different currents, some of the current is flowing through a second path. On an aircraft, that second path is often a wire whose insulation has chafed (worn through by rubbing) against the airframe, the aircraft's metal structure. Treat the difference as a fault to find, not as meter error.
Total Resistance
In a series circuit, resistance adds up. Each part adds its own opposition to the same current, one part after another, so the total resistance is the sum of every resistance in the path.
Rt = R1 + R2 + Rn
Series Resistance
60 Ω total
The circuit starts with 10, 20 and 30 ohm resistors, 60 ohms in total. Add or remove a resistor and watch the total resistance change.
Lower
Remove a resistor and close the gap
The total resistance goes down, and the current goes up.
Stops
Remove a resistor and leave the gap
The gap is a break in the path, called an open, and the current stops.
Every part of an aircraft circuit adds to this sum: the wire, each splice (a joint that connects two wires), each connector (a plug and socket that let the wiring be taken apart), the switch and the ground terminal (the fitting that connects a ground wire to the aircraft structure). A clean, tight connection adds almost nothing, and a corroded or loose one adds more. The corroded terminal lug in the Resistance lesson, a metal fitting squeezed onto the end of a wire so it can be bolted in place, added 0.90 ohm.
Voltage Drops
A voltage drop is the voltage across one part while current flows through it. It is the share of the source's pressure used to push the current through that part. In a series circuit, the voltage drops add up to the source voltage.
Et = E1 + E2 + En
This is Kirchhoff's voltage law, which you learned in the Voltage lesson: the sum of the voltage drops around a closed loop equals the source voltage.
Volts above the source's negative side
Source positive sideSource negative side
2.77 + 2.08 + 4.15 = 9.00 V
FIG 5 The voltage falls one step at each resistor. The steps add up to the 9 V source, and the largest resistor takes the largest step.
FIG 6 A 24 V source and three voltage drops. Two of the drops are known. Source: FAA-H-8083-30B, Figure 12-87.
Check your understanding
In this circuit the source is 24 V, and two of the drops are 12 V and 10 V. What is the third drop, E3?
Opens in a Series Circuit
An open is a break in the path, such as a burned-out lamp filament (the thin wire inside the lamp that glows) or a wire that has come loose. An open has infinite resistance, so no current flows through it. A series circuit has only one path, so one open stops the current everywhere, and every load goes dead at the same moment.
FIG 7 Three lamps in series on 28 V. When lamp 3 opens, the current stops in every part of the circuit at the same instant, and all three lamps go dark.
Effect of an Open
The open has infinite resistance, so the total resistance of the path is infinite.
The current is the source voltage divided by an infinite total resistance, so the current is zero.
Each good lamp drops E = I × R. With the current at zero, each good lamp drops 0 V.
This is why aircraft loads that must keep working when another load fails are never wired in series with each other. Some older holiday light strings were wired in series, and one burned-out bulb darkened the whole string. If the aircraft lights were wired in series, a failed landing light would also turn off the navigation lights, the red, green and white position lights on the wingtips and tail. The Parallel Circuits lesson shows how aircraft loads are wired instead.
Check your understanding
Four lamps are wired in series, and one filament opens. What happens to the other three?
Troubleshooting
Finding an Open
You can find an open with a voltmeter while the circuit is powered.
Tracing an Open with a Voltmeter
The resistor has burned open. With the switch on, the lamp still does not light, because the only path is broken.
Put the voltmeter across the lamp. It reads 0 V. No current flows, so the lamp drops no voltage, and a reading of 0 V tells you the lamp is not the open.
Put the voltmeter across the open resistor. It reads the battery voltage. The good parts drop 0 V, and the drops still add up to the source, so the whole source voltage appears across the open.
FIG 8 An open circuit, a voltmeter across the lamp, and a voltmeter across the open resistor. Adapted from FAA-H-8083-30B, Figures 12-174 to 12-176 (switch redrawn closed).
With the power on and an open in a series circuit, a voltmeter across a good part reads 0 V, and a voltmeter across the open reads the full source voltage.
Practice problem
Three lamps are wired in series on a 28 V supply, and all three are dark. With the power on, you read 0 V across lamp 1, 0 V across lamp 2 and 28 V across lamp 3. Which lamp is open?
FIG 9 The three lamps in series with lamp 3 open. The voltmeters read 0 V, 0 V and 28 V.
WarningMeasuring voltage drops with the power on means working on a live circuit. Use test leads in good condition, keep your other hand away from the circuit, and know which circuit breaker powers the circuit before you start.
Added Resistance
When resistance is added to a series circuit, the total resistance goes up and the current goes down. Current has an indirect relationship with resistance: when one goes up, the other goes down.
FIG 3 The 12 V circuit with R1, 10 ohms, and R2, 30 ohms. Source: FAA-H-8083-30B, Figure 12-82.
0.3 A
40 ohms total
The circuit as drawn: 12 V across 10 + 30 ohms.
0.15 A
80 ohms total
When the total resistance doubles, the current falls to half.
0.6 A
20 ohms total
When the total resistance is cut in half, the current doubles.
Source: FAA-H-8083-30B, Series DC Circuits, pages 12-34 and 12-35, the circuit in Figure 12-82.
Changes in Current
Each card is a change to a series circuit. Sort it by what the change does to the current in the one path.
Current rises
Total resistance falls.
Tap the bucket where the card belongs. On a computer you can also drag the card.
Current falls
Total resistance rises, and current still flows.
Current stops
The path is open, with infinite resistance.
Which bucket does this card belong in?
On the aircraft
The Landing Light Circuit
On the aircraft, the landing light is wired in series with the other parts of its circuit. From the bus, the current has one path: through a circuit breaker, the feed wire, the switch, a connector, the lamp, a ground wire and a ground terminal on the structure, and back to the battery through the structure.
Loading the 3D circuit.
Drag to turn the circuit. Select a numbered part to read what it does, then choose a condition.
FIG 10 A landing light circuit in a wing, as one series path. On smaller aircraft, landing lights usually sit midway along the leading edge, the front edge, of each wing. Source for the location: FAA-H-8083-31B, page 9-101.
On the aircraft
Allowable Voltage Drop
The wiring and connections of a circuit, from the bus out to the load and from the load back to its ground on the structure, always drop a little of the voltage. For that reason, a load never gets the full bus voltage. The Federal Aviation Administration (FAA) sets a limit for how much the wiring and connections may drop.
Table 11-6, in volts
System voltage
Continuous operation
Intermittent operation
14
0.5
1
28
1
2
115
4
8
200
7
14
FIG 11 Allowable voltage drop between the bus and the equipment's ground connection, in volts. The equipment is the load. Source: FAA Advisory Circular 43.13-1B, Change 1, Table 11-6, page 11-21.
Advisory circular (AC)
A guidance document the FAA publishes. AC 43.13-1B gives methods the FAA accepts for inspection and repair, and it is used when the aircraft manufacturer gives no instructions for the job. Here AC means advisory circular, not alternating current.
Continuous operation
A load that can stay on for more than two minutes at a time, such as a radio.
Intermittent operation
A load that runs for no more than two minutes at a time, such as the motors that move the landing gear or the flaps.
On a 28 V system, the wiring and connections of a load's circuit may drop no more than 1 V for continuous operation, or 2 V for intermittent operation.
A limit set by the aircraft or equipment manufacturer comes first. To check a circuit, AC 43.13-1B says to measure the voltage drop across it: if the drop is within the limit, the resistance of the circuit is acceptable.
Check your understanding
The wiring and connections of a lamp circuit on a 28 V system drop 1.68 V. What does Table 11-6 tell you?
Calculating Total Resistance and Current
To find the current in a series circuit, find the total resistance first. Then use Ohm's Law on the whole circuit: the total current is the source voltage divided by the total resistance.
Rt = R1 + R2 + Rn It = Et / Rt
FIG 12 Three resistors, 20, 15 and 30 ohms, in one series loop on a 9 V source.
Worked example
Add the resistances. Rt = 20 + 15 + 30 = 65 ohms.
Divide the source voltage by the total resistance. It = 9 V / 65 ohms = 0.13846 A. Keep these digits for the next page.
Check the answer. 65 ohms is larger than the largest resistor, 30 ohms, as it must be in series. If Rt comes out smaller than the largest resistor, you made a mistake: add the resistances again.
The same 0.13846 A flows through all three resistors.
When you work this by hand, 9 divided by 65 is often cut short to 0.13 A. That is close, but carry all the digits through the problem and round only at the end, because cutting the current short makes the drops on the next page add up to less than the source.
Practice problem
Resistors of 12, 33 and 47 ohms are wired in series across a 9 V source. What current flows?
Calculating Voltage Drops
Each part's voltage drop is the circuit current times that part's resistance. The current is the same through every part, so the largest resistance takes the largest drop.
Ex = It × Rx
Ex is the drop across any one part, and Rx is that part's resistance.
FIG 13 The same 20, 15 and 30 ohm circuit, with a bar for each drop.
Worked example
E1 = 0.13846 A × 20 ohms = 2.77 V
E2 = 0.13846 A × 15 ohms = 2.08 V
E3 = 0.13846 A × 30 ohms = 4.15 V
Check: 2.77 V + 2.08 V + 4.15 V = 9.00 V. The drops add up to the source, and the 30 ohm resistor took the largest drop.
Rounding Too Early
9.00 V
Current carried as 0.13846 A
2.77 + 2.08 + 4.15 = 9.00 V
8.45 V
Current cut short to 0.13 A first
2.60 + 1.95 + 3.90 = 8.45 V
The drops add up to 8.45 V, close to 9 V, only because the current was cut short to 0.13 A before multiplying. Carry all the digits and round only at the end, and the drops add up to the 9 V source.
Voltage Drop Practice
Resistor values and currents are often written with a prefix. Change each value to ohms and amperes before you multiply.
FIG 14 Three resistors in series, 1 kΩ, 3 kΩ and 5 kΩ, with a current of 1 mA. kΩ means kilohms: 1 kΩ is 1,000 ohms. mA means milliamps: 1 mA is 0.001 A. Source: FAA-H-8083-30B, Figure 12-83.
Kilo (k)
One thousand. 3 kΩ is 3 × 1,000 = 3,000 ohms.
Milli (m)
One thousandth. 1 mA is 1 / 1,000 = 0.001 A.
Practice problem
The current in this circuit is 1 mA. What is the voltage drop across R2, the 3 kΩ resistor?
Landing Light Calculations
Now work the landing light circuit. On a 28 V bus, the lamp is 7.84 ohms when it is lit and hot. When the circuit is in good condition, the wiring, circuit breaker, switch, connector and ground together add 0.25 ohm in series with it. By itself on 28 V, this 100 W lamp would draw 3.57 A. The wiring and connections in series with it make the current a little lower.
FIG 15 The landing light circuit with its two resistances: the lamp, 7.84 ohms, and the wiring and connections, 0.25 ohm in all.
Worked example
Rt = 7.84 ohms + 0.25 ohm = 8.09 ohms
It = 28 V / 8.09 ohms = 3.461 A
Lamp: 3.461 A × 7.84 ohms = 27.13 V
Wiring and connections: 3.461 A × 0.25 ohm = 0.87 V
Check: 27.13 V + 0.87 V = 28.00 V
Practice problem
A loose connector pin raises the wiring and connections from 0.25 ohm to 1.50 ohms. What voltage does the lamp get?
Corroded Ground Terminal
Corrosion at the ground terminal adds 1.75 ohms to the one path, so the wiring and connections rise from 0.25 ohm to 2.00 ohms. Predict what that does, then check the numbers.
FIG 16 The landing light circuit with a corroded ground terminal.
Prediction: Corroded Ground
Predict each change.
The current
The voltage across the lamp
The voltage across the wiring and connections
Value
Normal
Corroded ground terminal
Wiring and connections
0.25 ohm
2.00 ohms
Total resistance
8.09 ohms
9.84 ohms
Current
3.461 A
2.846 A
Across the lamp
27.13 V
22.31 V
Across the wiring and connections
0.87 V
5.69 V
Sum of the drops
28.00 V
28.00 V
This example treats the lamp as a fixed 7.84 ohms. A real filament's resistance falls as it cools, so a real lamp's numbers differ somewhat, but every change goes the same way.
Voltage Divider
A series circuit divides the source voltage among its parts in proportion to their resistance. When one resistance goes up, its share goes up, while the current and every other share go down. The drops still add up to the source.
Voltage divider
A set of resistors in series, used to get a smaller voltage from a larger source. The FAA handbook notes that series circuits are used as voltage dividers.
Prediction: Doubling R2
The divider below starts at 20, 15 and 30 ohms on 9 V. If you double R2 from 15 to 30 ohms, what happens to the current and to the drop across R2?
Move the R2 slider to 30 ohms and check your prediction. Then try a small R2 and a large one.
Voltage Divider Circuit
9 V source, R1 20 Ω, R2 variable, R3 30 Ω
15 Ω
Rt
65Ω
It
0.13846A
E1
2.77V
E2
2.08V
E3
4.15V
Sum
9.00V
It = 9 V / 65 Ω = 0.13846 A. E2 = It × R2 = 2.08 V. E1 + E2 + E3 = 2.77 + 2.08 + 4.15 = 9.00 V. R2 takes 23 percent of the source.
FIG 17 Change R2 and watch the total resistance, the current and all three drops change. The drops always add up to the source. The readouts are rounded, so the last digit of a sum can be off by 0.01 V.
Measuring a Series Circuit
Now measure a series circuit yourself. A 9 V source feeds four 100 ohm resistors in series, with a connector, P1, in the middle of the four. Read the total resistance with switch S1 open, read the drops with the power on, then pull P1 and find the open.
Each part in the lab carries a label.
BT1the battery
S1the switch
P1the connector
R1 to R4the four resistors
NEVER MEASURE RESISTANCE ON A POWERED CIRCUIT.
The first two steps use the ohmmeter, so switch S1 stays open. An ohmmeter sends its own small current through the part. On a powered circuit it gives a false reading and can be damaged.
Prediction: R1 with S1 Closed
With S1 closed and the power on, what will the meter read across R1?
Follow the six steps in the panel beside the circuit. Each step checks itself, and the reading log records your meter reading when the step passes. Select Meter in the lab's top bar to bring up the meter, and select a part to change its value.
Steps done: 0 of 6. Your readings are recorded in the log beside the circuit.Open in a new tab
R1...× 4 =...Four equal drops add up to the source.
Lab ResultsThe four 100 ohm resistors added up to 400 ohms, and each dropped a quarter of the 9 V, 2.25 V. Pulling P1 stopped the current everywhere: R1 read 0 V, and the whole 9 V appeared across the open connector. You use the same voltmeter reading to find an open in aircraft wiring.
Applying the Procedure
This page applies the lesson to the dim landing light from the first page. The lamp is new, the circuit breaker has not opened, and the bus reads 28 V.
FIG 18 Select a step to see where the meter leads go and what the meter reads.
The lamp was not the fault. The corroded ground terminal added resistance in series with the lamp and dropped 4.98 V, so the lamp got less voltage.
Check
Five questions, three answers each. Each answer tells you why it is right or wrong.
4 of 5
Needed to pass
1IdentifyIdentify a series circuit by its one path, where the current is the same at every point.
2CalculateCalculate the total resistance and the total current.
3CalculateCalculate each voltage drop and confirm that the drops add up to the source.
4PredictPredict what an open, or added resistance, does to the current and every drop.
Question 1 of 5
0 of 5
ResultsResults
From this lesson
01A series circuit has one path, and the current is the same at every point in it.
02Rt = R1 + R2 + Rn, and It = Et / Rt.
03Each drop is It × Rx, and the drops add up to the source voltage.
04An open stops the current everywhere. Added resistance lowers the current and changes every drop.
Select any row to re-read its feedback.
Field Card
You can now identify a series circuit by its one path, where the current is the same at every point.
You can now find the total resistance by adding every resistance in the path, and the total current with It = Et / Rt.
You can now find each voltage drop with Ex = It × Rx, and confirm that the drops add up to the source voltage.
You can now predict that one open stops the current everywhere, and that added resistance lowers the current and changes every drop.
Path
Pathsone
Currentthe same at every point
Two readings differlook for a second path
Totals
Total resistanceRt = R1 + R2 + Rn
Total currentIt = Et / Rt
CheckRt is larger than the largest resistor
Drops
Each dropEx = It × Rx
All dropsEt = E1 + E2 + En
Roundingcarry the digits, round at the end
Faults
Openthe current stops, good parts read 0 V, and the open reads the source
Added resistancethe current falls, and that part's drop rises
28 V limit1 V continuous, 2 V intermittent
Troubleshooting
With the power on, measure the voltage drop across each part of the circuit in turn. The part that drops more voltage than it should has the added resistance. Measure before you replace a part.
