Resistance

• Resistance formula: R = ρL/A — resistivity ρ, length L, area A.
• Series combination: R_eq = R₁ + R₂ + …; same current.
• Parallel combination: 1/R_eq = 1/R₁ + 1/R₂ + …; same voltage.
• Resistivity — material property; unit Ω·m; silver low, nichrome high.
• Heating effect link: H = I²Rt.

1. R = ρL/A — doubling length doubles R; doubling area halves R.
2. Series — R_total = R₁ + R₂; I same everywhere; V divides.
3. Parallel — 1/R_total = 1/R₁ + 1/R₂; V same across each; I divides.
4. Resistivity (ρ) — independent of shape; depends on material and temperature.
5. Conductors — low ρ (copper, aluminium); insulators — very high ρ.
6. Two equal resistors in parallel — R_eq = R/2.
7. Household wiring — appliances in parallel so each gets 220 V.
8. Heating element — nichrome high ρ, high melting point.
9. Series disadvantage — one failure breaks circuit; bulbs dim when more added.
10. NCERT activity — compare brightness of bulbs in series vs parallel.

Three resistors 2 Ω, 3 Ω, 6 Ω in parallel — find equivalent resistance

Given: R₁ = 2 Ω, R₂ = 3 Ω, R₃ = 6 Ω (parallel)
Step 1 — 1/R_eq = 1/2 + 1/3 + 1/6
Step 2 — LCM 6: 1/R_eq = 3/6 + 2/6 + 1/6 = 6/6 = 1
Step 3 — R_eq = 1 Ω
Step 4 — Parallel R_eq always less than smallest resistor (1 < 2) ✓
Conclusion: equivalent resistance is 1 Ω.

• Adding resistances in parallel like series (R₁ + R₂ wrong).
• Misconception: parallel means more resistance (actually less).
• Forgetting same current in series, same V in parallel.
• Confusing resistance with resistivity.
• Not taking reciprocal after summing 1/R terms.

• Write formula for R in terms of ρ, L, A.
• Two 10 Ω resistors — R_eq in series? In parallel?
• Why are home appliances connected in parallel?
• How does doubling wire length affect R?

Open the Practice tab for graded questions on Resistance.