DC Circuits
Ohm's law, Kirchhoff's voltage and current laws; the significance of internal resistance; series, parallel and series-parallel networks.
DC circuits — summary notes
Free- 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.
- 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)
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.
A 24 V supply drives 3 A through a circuit. What is its resistance?
R = V / I = 24 / 3 = 8 Ω.
Ohm's law — V = I × R
FreeSeries vs parallel resistance
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Kirchhoff's laws
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The voltage divider
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DC circuits concept map
FreeDC Circuits
DC circuits quiz
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