Basic Circuit Laws: Ohm's law

Basic Circuit Laws: Ohm's law

1. Statement — Ohm's Law (1827, Georg Ohm)

Ohm's law states: at constant temperature, current $I$ through a conductor is directly proportional to voltage $V$ across it, with proportionality constant $R$ (resistance):

where $R$ in ohms (Ω). In terms of conductance $G=1/R$ (siemens S):

For AC phasors:

where $Z$ is impedance (complex).

2. Conditions and Limitations

• Holds for linear, bilateral, passive conductors at constant temperature (metals at constant $T$).
• Fails for non-linear elements (diode, transistor, filament when $T$ changes), and for non-ohmic materials (electrolyte, gas discharge), and at high fields where $R$ varies.
• Generalized forms:

(microscopic, $σ=1/ρ$ conductivity), and

for $L$,

for $C$ are not Ohm's but analogous.

3. Power and Energy from Ohm's Law

Combine $P=VI$ with $V=IR$:

(heat); energy over time $t$:

This explains Joule heating in resistors; $P$ always positive (absorbing) for $R>0$.

4. Worked Examples

(a) Resistor 20Ω with V=100V: I=5A, P=500W ✓

(b) Need to limit current to 0.5A at 12V: R= V/I=24Ω ✓

(c) Two resistors series 10Ω+20Ω at 30V: total R=30Ω, I=1A, V10=10V, V20=20V (divider) ✓

(d) Check non-ohmic: diode V=0.7V at I=10mA ⇒ R_dynamic=70Ω, but at V=0.8V I=100mA ⇒ R=8Ω not constant ⇒ no Ohm's law.

5. Exam Points

• State $V=IR$ with $R$ constant at constant $T$ — 3-5 marks, very frequent (almost certain to ask).
• Show $J=σE$ — 3 marks, frequent.
• Mention limitations (non-linear, $T$ dependence) — 5 marks, frequent.
• Solve $V=IR$ for series/parallel — 5 marks, frequent.
• Derive $P=I²R$ — 3 marks.