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Concept · Electromagnetism
DC circuits
current I=q/t, resistance R=ρ·L/A, Ohm's law U=IR, series (equal I, voltage divides; R=sum) and parallel (equal U, current divides; 1/R=sum, two-resistor shortcut), power P=UI=I2R=U2/R, Joule heating Q=I2Rt, EMF & internal resistance (terminal voltage, max power at R=r), non-ohmic devices (motor Pmech=UI-I2R)
Switches you to Physics
Named traps
21 ways this goes wrong.
Each is a named misconception the questions are built to catch. Open one for the move that tempts, and the fix.
- Adding parallel R raises totalThinks adding a resistor in parallel increases the overall resistance instead of decreasing it.→
- Current equal in parallel branchesAssumes equal current through unequal parallel branches instead of the current dividing in inverse proportion to resistance.→
- Current used up in circuitBelieves current is consumed by components so less returns to the battery than left it.→
- EMF equals terminal voltage alwaysTreats EMF and terminal voltage as identical even when current is flowing.→
- Internal resistance ignoredSets terminal voltage equal to EMF, ignoring the Ir drop across the source's internal resistance.→
- Metal resistance drops with heatBelieves a metallic conductor's resistance falls as its temperature rises.→
- Output power assumed monotonic in RBelieves the power delivered to the external resistor keeps rising as R increases, missing that it peaks when R equals the internal resistance r.→
- Parallel R exceeds smallest branchReports an equivalent parallel resistance larger than the smallest branch resistance.→
- Parallel resistance added directlyAdds parallel resistances directly instead of combining reciprocals (or misuses the two-resistor product-over-sum shortcut).→
- Power formula variant mismatchedPicks the wrong P formula among UI, I2R, U2/R for the known quantities, e.g. uses I2R when only U and R are given.→
- Power scaling taken as linearAssumes power changes in proportion to voltage (or current) rather than to V2 (or I2) when R is fixed, e.g. doubling V doubles instead of quadruples P.→
- R independent of lengthIgnores the length dependence in R=ρ·L/A when comparing wires.→
- R proportional to areaTreats resistance as increasing with cross-sectional area instead of R proportional to L/A.→
- R read as U/I proportionalityTreats R=U/I as meaning resistance changes when the applied voltage changes, rather than R being a fixed property of the ohmic component.→
- Rated power used at wrong voltageUses a device's rated power directly at a different operating voltage, instead of treating R as fixed and recomputing P=U2/R.→
- Resistivity equals resistanceUses resistivity ρ and resistance R interchangeably, ignoring the L/A geometry factors.→
- Running motor treated as ohmicApplies U=IR or P=U2/R to a running motor, ignoring that it does mechanical work so Pmech=UI-I2R and it is non-ohmic.→
- Stretched-wire area change ignoredWhen a wire is stretched to double its length, doubles R but ignores that the area halves, missing the net factor of 4.→
- U=IR rearranged wrongRearranges Ohm's law incorrectly, e.g. writes I=UR or R=UI.→
- Voltage divider ratio invertedInverts the series voltage-divider ratio, assigning the larger share of voltage to the smaller resistor.→
- Voltage equal across series resistorsAssumes the same voltage across each series resistor regardless of their resistances.→
Key formulas
No formula sheet is matched to this concept yet. Work it from first principles, and watch the traps.
Shaky underneath?
If the concept underneath still feels loose, patch it here before coming back to CSCA questions.
FoundationsPhysics 2 breadthMechanics foundations