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DC Circuits, Resistors, Optics & Wave Physics

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1. Ohm's Law and Series vs Parallel Circuits

Direct current circuits route charge carriers through networks of resistors according to Ohm's law and Kirchhoff's conservation rules.

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Direct current electric circuits with series and parallel resistor topologies

Wikimedia Commons / inductiveload / Public Domain

Ohm's Law

V = I · R

Potential difference across an ohmic conductor is directly proportional to current

Series Circuits

R_eq = R₁ + R₂ + ... + R_n · Same current I through all components

Total equivalent resistance is always strictly greater than any individual resistor

Parallel Circuits

1/R_eq = 1/R₁ + 1/R₂ + ... + 1/R_n · Same voltage V across all branches

Total equivalent resistance is always strictly less than the smallest branch resistor

Worked example

1Calculate total equivalent resistance for two resistors, 6 ohms and 12 ohms, connected in parallel.
2Apply parallel formula: 1/R_eq = 1/6 + 1/12 = 2/12 + 1/12 = 3/12 = 1/4.
3Reciprocal gives R_eq = 4 ohms.
4If connected in series, R_eq = 6 + 12 = 18 ohms.

For the exam

Series Circuit: Current I is identical through all components; Total Voltage V = V1 + V2; Req = R1 + R2 (Req > any single resistor)
Parallel Circuit: Voltage V is identical across all branches; Total Current I = I1 + I2; 1/Req = 1/R1 + 1/R2 (Req < any single branch resistor)
Power Dissipation: P = I² × R = V² / R

1.In a parallel electrical circuit, voltage across each branch is equal.

2.Connecting resistors in parallel increases the total equivalent resistance.

3.Two 10-ohm resistors connected in series give an equivalent resistance of 20 ohms.

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