Resistance & Resistors
Resistance and the factors affecting it; specific resistance; the resistor colour code; conductance; positive and negative temperature coefficients; resistors in series and parallel; the Wheatstone bridge.
Resistance & resistors, summary notes
- Resistance depends on the material and the dimensions of the conductor: R = ρL / A. Longer means more resistance; thicker (greater area) means less.
- Resistivity ρ is a property of the material, measured in ohm-metres. Copper and silver have very low resistivity.
- Metals have a positive temperature coefficient, resistance rises as they get hotter. Carbon and semiconductors have a negative coefficient.
- Fixed resistors are marked with a 4-band or 5-band colour code; the last band is the tolerance.
- Variable resistors: a rheostat is a two-terminal current control, a potentiometer is a three-terminal voltage divider.
- ⚠ Exam trap: thicker wire means LOWER resistance. A common distractor reverses the area relationship.
- Resistance of a conductor
- R = ρL / A
- Temperature effect
- R₂ = R₁[1 + α(t₂ − t₁)]
- Wheatstone bridge at balance
- R₁/R₂ = R₃/R₄
A wire's length is doubled and its cross-sectional area is halved. What happens to its resistance?
R = ρL/A. Doubling L doubles R; halving A doubles R again. The resistance becomes 4 times the original.
Why does a filament lamp draw a large surge current when first switched on?
The tungsten filament is cold, and metals have a positive temperature coefficient, so its resistance is low. As it heats, resistance rises and current settles to its normal value.
The Wheatstone bridge
Resistance concept map
Resistance & Resistors
Resistance & resistors quiz
Resistance & Resistors, quiz
1. Three 30 ohm resistors are connected in parallel. The total resistance is:
10 ohms90 ohms30 ohms2. A wire of 2 ohms is stretched to twice its length with the same volume of material. Its new resistance is:
8 ohms4 ohms1 ohm3. A 12 ohm and a 4 ohm resistor are in parallel. The combined resistance is:
3 ohms16 ohms8 ohms4. If a conductor's cross-sectional area is doubled, its resistance:
HalvesDoublesIs unchanged5. A wire's length is doubled and its area halved. Its resistance becomes:
Four times the originalTwice the originalHalf the original6. Metals have a temperature coefficient of resistance that is:
PositiveNegativeZero7. The unit of resistivity is the:
Ohm-metreOhmOhm per metre8. In a 4-band resistor colour code, the fourth band indicates:
ToleranceThe multiplierThe first significant figure9. A filament lamp draws a large surge at switch-on because:
The cold filament has a low resistanceThe supply voltage is momentarily higherThe filament is initially open-circuit10. A three-terminal variable resistor used to divide voltage is a:
PotentiometerRheostatThermistor