Resistors: series, parallel, potential dividers and source resistance
Ohm's law with milli and kilo, combining two or three resistors, the potential divider, tolerances, and why a battery's voltage drops under load.
Key points
Summary
| Circuit | Formula | Remember |
|---|---|---|
| Ohm's law | V = I × R | Convert k and m first |
| Series | R = R1 + R2 + R3 | Same current |
| Parallel | 1/R = 1/R1 + 1/R2 + 1/R3 | Less than the smallest |
| Potential divider | Vout = Vin × R2 ÷ (R1 + R2) | Output across R2 |
| Source resistance | V = EMF − I × r | Drop grows with current |
Quick check
What is the total resistance of 100 Ω, 220 Ω and 330 Ω in series?
- 650 Ω
- 65 Ω
- 550 Ω
- 50 Ω
Two 100 Ω resistors are connected in parallel. What is the combined resistance?
- 200 Ω
- 50 Ω
- 100 Ω
- 25 Ω
A 12 V supply feeds a potential divider of 3 kΩ (top) and 1 kΩ (bottom). What is the output across the 1 kΩ resistor?
- 9 V
- 4 V
- 3 V
- 12 V
Work it out
Try each one first, then open it to see the working.
Find the total resistance of 100 Ω and 300 Ω in parallel.
- 1/R = 1/100 + 1/300
- 1/R = 3/300 + 1/300 = 4/300
- R = 300 ÷ 4
A 220 Ω resistor is in series with 100 Ω and 100 Ω in parallel. Find the total.
- Parallel pair = 100 ÷ 2 = 50 Ω
- Total = 220 + 50
Find the output of a potential divider: 9 V supply, R1 = 6.8 kΩ, R2 = 2.2 kΩ.
- Vout = Vin × R2 ÷ (R1 + R2)
- Vout = 9 × 2.2 ÷ 9.0
What current flows through 2.2 kΩ with 11 V across it?
- I = V ÷ R
- I = 11 ÷ 2200 = 0.005 A
On air
- Measure your power supply's voltage with no load, then while transmitting, and work out the drop.
- Measure three resistors of the same marked value and compare them with the tolerance band.
- Practise the parallel formula until you can do it without a calculator for equal values.
Video transcript
Resistor calculations appear in almost every Intermediate paper. In this lesson: Ohm's law with milli and kilo, series and parallel combinations, the potential divider, and why a battery's voltage falls as you draw current.
Ohm's law says voltage equals current times resistance. Rearrange it to find any one of the three: current is voltage divided by resistance, and resistance is voltage divided by current. Watch the prefixes. Kilo means a thousand, so four point seven kilohms is four thousand seven hundred ohms. Milli means a thousandth, so twenty milliamps is zero point zero two amps. For example, if twelve volts drives sixty milliamps through a resistor, the resistance is twelve divided by zero point zero six, which is two hundred ohms.
In series, the same current flows through every resistor, so you simply add the values: one hundred, two hundred and twenty and three hundred and thirty ohms make six hundred and fifty ohms. In parallel, add the reciprocals, then take the reciprocal of the answer. The total is always less than the smallest resistor. Two equal resistors in parallel give half the value, so two one hundred ohm resistors make fifty ohms. For combined circuits, work out the parallel group first, then add the series parts.
Two resistors in series across a supply share the voltage in proportion to their values. This is a potential divider. The output is taken across the lower resistor, and equals the input voltage times the lower resistor, divided by the total of both. With twelve volts across three kilohms and one kilohm, the output across the one kilohm resistor is twelve times one quarter, which is three volts. You can use kilohms throughout, as long as you use the same unit for both resistors.
A battery's electromotive force, or E M F, is its voltage when no current flows. Every source also has internal resistance, so when you draw current, some voltage is lost inside it. The potential difference at the terminals is the E M F minus the current times the internal resistance. A twelve volt battery with half an ohm of internal resistance, supplying four amps, loses two volts and delivers ten. Finally, components have a tolerance. A one hundred ohm resistor marked five percent may measure anywhere from ninety five to one hundred and five ohms.
This is one of 23 lessons in the Intermediate course
The full course adds drills, flashcards, a revision sheet for every lesson and 5 full mock exams.