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Playbook

Electricity and Magnetism

93 q · 22% HARD — the bank's #1 HARD pool. Combination of Resistors (16 q at 38% HARD) carries the chapter. Series-vs-parallel resistor reasoning, V=IR, P=I²R, charge-in-magnetic-field force direction, electrostatics shell theorem. The single highest-leverage chapter for HARD-pool prep.

questions in the bank
93
tagged HARD
22%
subtopic(s)
9
worked examples
2

When you’ll see it

Any resistor-network reduction, a P = V²/R / I²R / VI choice, a charge-in-magnetic-field force direction, an electrostatics shell or capacitor, or a Fleming's left/right hand rule.

How this chapter is tested

93 q in 10 years · 22% HARD. The bank's #1 HARD pool by absolute count. Nine subtopics: Combination of Resistors (16 q · 38% HARD), Magnetism and Magnetic Effects (16 q), Electrical Devices (15 q), Electrostatics (13 q), Electrical Power/Energy/Heating (10 q · 30% HARD), Electric Current and Ohm's Law (9 q), Resistance and Resistivity (6 q), Magnetic Force and Fleming's Rules (5 q · 40% HARD), Cells/EMF/Kirchhoff (3 q).

Combination of Resistors is the marquee subtopic. R_series = sum, R_parallel = reciprocal sum. For two equal R in parallel: R/2. For N equal R in parallel: R/N. The 'wire of resistance R cut into N equal pieces and reconnected' shape: each piece R/N, N in parallel ⟹ R/N². Heat dissipation P = V²/R for fixed V: parallel (smaller R) dissipates MORE. Ratio P_parallel/P_series with same V and two equal R: 4.

Magnetism HARD shape: a charged particle enters a magnetic field. Force F = qv × B (vector cross product). Direction by right-hand rule for positive charge (thumb=v, fingers=B, palm=F); opposite for negative. If v ∥ B, force = 0; if v ⊥ B, magnitude qvB, particle moves in circle. Trap: mixing up Fleming's left-hand (motor — F from V and B) with right-hand (generator — induced V from F and B).

The sub-skills

The rules and habits that decide whether you get a question right.

  • Series / parallel reduction

    Series: R_eq = R₁+R₂. Parallel: 1/R_eq = 1/R₁+1/R₂ ⟹ for two: R₁R₂/(R₁+R₂). Iterate from the innermost combination outward. For ladder/infinite networks, exploit self-similarity: R_∞ = R + (R · R_∞)/(R+R_∞).

  • Power-form selection

    P = VI (always works). P = I²R (use when I and R given, fixed I scenario). P = V²/R (use when V and R given, fixed V scenario). For constant V: smaller R ⟹ more P. For constant I: larger R ⟹ more P.

  • Lorentz force direction

    F = qv × B. Magnitude qvB sinθ. Direction by right-hand rule for +q; opposite for −q. Positive and negative charges deflect OPPOSITE directions in same field.

  • Resistivity and stretching

    R = ρL/A. Stretching keeps volume constant (V = LA), so doubling L halves A and R quadruples (R ∝ L²). Bending or coiling doesn't change R.

2 worked examples from the bank

Real past-year questions illustrating the playbook. Click to reveal options + solution.

Example 1Electricity and MagnetismHARD
Two conducting wires of the same material and of equal lengths and equal diameters are first connected in parallel and then in series in a circuit across the same potential difference. The ratio of heat produced in parallel and series combinations is

[Q128 · Apr · 2025]

Example 2Electricity and MagnetismHARD
Three wires each of length LL, area AA and resistivity ρ\rho are connected (two in parallel X to Y, one Y to Z). A single wire of same resistivity replaces them without changing resistance X to Z. If new wire has length L1L_1 and area A1A_1, which is correct?

[Q72 · Apr · 2026]

Traps to expect

Distractor shapes specific to this chapter. The page-wide Traps section covers the bank-level patterns.

  • Parallel vs series, ratio inverted

    P_parallel/P_series = 4 (for two equal R, same V). Picking 1/4 (correct magnitude, inverted) is the dominant wrong option. Always reason 'which has smaller R_eq' first.

  • Negative-charge force direction

    Right-hand rule gives direction for POSITIVE charges. For negative charges, reverse the direction. Wrong options use right-hand rule on a negative charge without flipping.

  • P = I²R vs P = V²/R when comparing

    Don't use I²R when comparing two resistors carrying DIFFERENT currents (series with different parallel branches). Don't use V²/R when they have DIFFERENT V across them. P = VI always works.

Drill every electricity and magnetism question

93 questions from the bank, scoped to 9 bundled subtopics.

Drill the 93 questions

Related playbooks

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