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Section 3.6

DC Circuits

Ohm's law, Kirchhoff's voltage and current laws; the significance of internal resistance; series, parallel and series-parallel networks.

Notes

DC circuits — summary notes

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Main ideas
  • Ohm's law: V = I × R. Rearranged as I = V / R and R = V / I.
  • Kirchhoff's current law: the sum of currents entering a node equals the sum leaving it. Charge is conserved.
  • Kirchhoff's voltage law: around any closed loop, the sum of the EMFs equals the sum of the I·R drops. Energy is conserved.
  • In series: current is the same everywhere, voltages add, and resistances add.
  • In parallel: voltage is the same across each branch, currents add, and 1/R_T = Σ(1/R).
  • ⚠ Exam trap: two equal resistors in parallel give half the value of one. Total parallel resistance is always less than the smallest branch.
Key formulas
Ohm's law
V = I × R
Series resistance
R_T = R₁ + R₂ + R₃ …
Parallel resistance
1 / R_T = 1/R₁ + 1/R₂ + 1/R₃ …
Two resistors in parallel
R_T = (R₁ × R₂) / (R₁ + R₂)
Solved examples
  1. Two 10 Ω resistors in parallel are in series with a 5 Ω resistor. Find the total resistance.

    Parallel pair = (10 × 10)/(10 + 10) = 5 Ω. In series with 5 Ω gives R_T = 10 Ω.

  2. A 24 V supply drives 3 A through a circuit. What is its resistance?

    R = V / I = 24 / 3 = 8 Ω.

Simulation

Ohm's law — V = I × R

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Simulation

Series vs parallel resistance

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Simulation

Kirchhoff's laws

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Simulation

The voltage divider

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Mind map

DC circuits concept map

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DC Circuits

Quiz

DC circuits quiz

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