What a learner can do afterwards
- Calculates the total resistance of resistors in series and predicts the current
- Explains why two identical resistors in parallel halve the total resistance
- Predicts the supply-current change when a working lamp is added in parallel at unchanged supply voltage, and checks it in a supervised low-voltage circuit
1 · Read
In series, charge follows one unbranched path through every resistor. The same current flows through each. Add all resistor values to find total resistance. The supply voltage is shared in proportion to resistance. Treat connecting wires as having negligible resistance and fixed resistor values as unchanged by heating.
To predict current through series resistors, first add their resistance values. Then use I = V / R total: current in amperes (A) = supply voltage in volts (V) divided by total resistance in ohms. For example, 8 ohms and 16 ohms give 24 ohms. At 6 V, I = 6 / 24 = 0.25 A through both resistors.
Parallel branches join the same two points. When connected across the supply, each has its full voltage. Two identical resistors draw equal currents; together they draw twice one resistor's current. Total resistance is supply voltage divided by supply current, so doubling current at the same voltage halves resistance. Two 18 ohm resistors give 9 ohms in parallel; in series, add them to get 36 ohms.
Supply current is the sum of the parallel branch currents. For example, 0.10 A + 0.15 A = 0.25 A. Adding a working lamp at unchanged supply voltage adds its current; the other lamps keep their settled currents. Supply current rises, so total resistance falls. Check voltage and supply current before and after adding the branch. A real supply may lose voltage or limit current if overloaded.
An ammeter measures current and goes in series in the measured path. Its low resistance means connecting it across a supply can cause a short circuit and damage. A voltmeter goes across two points to measure their voltage difference. It has high resistance so it draws very little current and changes the circuit less. Use supervised low-voltage circuits with suitable components and meter ranges. Switch off before rewiring. Never experiment with household mains.
If a bulb fails by breaking the only current path in a series string, every bulb goes out. Some strings have bypasses, so bulb failure does not always break the path. Household appliances use parallel connections to receive supply voltage and switch separately, within the supply's limits.
Series resistances add. Parallel branch currents add. At unchanged supply voltage, adding a working parallel branch raises supply current and lowers total resistance.
Lesson, questions, worked solutions and flashcards written for this dataset.
Readings and flashcards written for this dataset. Video lessons credited to Khan Academy in the source catalog: Series and parallel circuits; Parallel resistors; Voltmeters and ammeters.
More to read
From resistance to current
Start a series calculation by listing every resistor on the unbranched path. Add those values before calculating current. For fixed resistors, use values that do not change during the calculation, and treat connecting-wire resistance as negligible.
Suppose a 3 V supply is connected to 50 ohm and 100 ohm resistors in series. The total is 150 ohms. Dividing 3 V by 150 ohms gives 0.02 A. Both resistors carry this current because neither has a separate branch.
The resistors share the supply voltage. Using voltage = current times resistance gives 1 V across the 50 ohm resistor and 2 V across the 100 ohm resistor. These drops add to 3 V. The larger resistor has the larger drop because the current through both is equal.
If another positive resistance is added in series while supply voltage stays unchanged, total resistance increases and current decreases.
Why an extra branch changes the total
Parallel branches connect between the same pair of points. When those points are the supply terminals, each branch has the supply voltage across it. Current from the supply divides between the branches and joins again afterwards.
Take two identical 40 ohm resistors across 4 V. Each branch carries 4 / 40 = 0.10 A. Supply current is 0.10 + 0.10 = 0.20 A. The resistance of the whole pair is supply voltage divided by supply current: 4 / 0.20 = 20 ohms. That is half the resistance of one resistor. For two or more positive, finite resistances in parallel, the total is less than the smallest branch resistance.
A working lamp added across an unchanged supply voltage draws an extra branch current. After temperatures settle, the other lamps keep their currents, so total current rises. A supply can lose voltage or limit current under a heavy load. Measure voltage as well as current when checking the prediction.
Parallel connections let household appliances receive supply voltage and switch separately, within the supply's limits. A series string depends on its shared path. A failed bulb stops all current only if it breaks that path without a bypass. Never experiment with household mains.
Comparing predictions with meter readings
An ammeter must carry the current being measured, so it goes in series in that path. To measure supply current, place it where the current has not yet divided between parallel branches, or after the branches rejoin. A voltmeter goes across the two points whose voltage difference you want.
An ammeter has low resistance to reduce the voltage drop it adds. A voltmeter has high resistance to draw little current. For ideal calculations, neglect wire and ammeter resistance and treat voltmeter current as zero. Do not treat voltmeter resistance as zero: that would connect a short circuit across the measured points.
For a paper prediction, connect two fixed 150 ohm resistors to 3 V. In series, total resistance is 300 ohms and current is 3 / 300 = 0.01 A. In parallel, total resistance is 75 ohms and supply current is 3 / 75 = 0.04 A.
To test these predictions, use a supervised low-voltage circuit with suitable components, a suitable current limit and suitable meter ranges. Switch off before rewiring. Check the supply voltage in each arrangement and compare the measured currents with the predictions. Real meters and resistor values can cause small differences. An ammeter across a supply can cause a short circuit and damage. Never use household mains.
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