Electric Circuits – Power, Energy, Dissipation & Non-Ohmic Devices

Core Electrical Quantities

• Charge (Q)

  • Measured in coulombs (C).

• Current (I)

  • Rate of flow of charge.

  • Units: amperes (A). $I=\frac{Q}{t}$

• Potential Difference / Voltage (V)

  • Energy transferred per unit charge.

  • Units: volts (V). $V=\frac{E}{Q}$

• Resistance (R)

  • Opposition to current. Units: ohms (Ω).

  • Ohm’s Law: $V = IR \;\;\Rightarrow\;\; I = \frac{V}{R}, \; R=\frac{V}{I}$

• Electrical Energy (E)

  • Total work done in moving charge through a potential difference. Units: joules (J).

  • General forms derived from combining $E = Pt$ with power formulas (below):

  • $E = P\,t$

  • $E = V I t$

  • $E = I^{2} R t$

  • $E = \frac{V^{2}}{R} t$

• Electrical Power (P)

  • Rate of energy transfer. Units: watts (W = J s⁻¹).

  • Three interchangeable forms (choose the one that matches given data):

  • $P = V I$

  • $P = I^{2} R$ (substitute $V = IR$ into $VI$)

  • $P = \frac{V^{2}}{R}$ (substitute $I = \tfrac{V}{R}$ into $VI$)

Essential Units & Conversions

• Standard exam requirement: always convert before substituting.

  • Time → seconds (s).

  • Current → amperes (A).

  • Voltage → volts (V).

• Energy: joules (J).

• Power: watts (W).

• Electrical Energy for billing: kilowatt-hours (kWh).

  • kWh is NOT a power unit; it is an energy unit used by utility companies.

  • Conversion:

  • $1\text{ kWh} = 1000\,\text{W} \times 3600\,\text{s} = 3.6 \times 10^{6}\,\text{J}$

• Typical exam conversion path:

  • Convert kW→W (×1000) and h→s (×3600), then put answer in J or vice-versa.

Systematic Problem-Solving Checklist

1. Write down GIVEN and NEEDED quantities.

2. Convert all data to SI units (A, V, Ω, s).

3. Select the shortest formula that links the knowns to the unknown.

4. Substitute, calculate, quote answer with unit.

Power Dissipation & Heating

• Dissipated Power = energy irreversibly lost as heat (and sometimes sound/light) in a component.

• Governed by $P = I^{2} R$ — explains why high current devices get hot.

• Observable facts:

  • Chargers, phones, laptops, hair-dryers all warm up because resistance causes power loss.

  • EMF of a supply is slightly larger than measured terminal voltage because some energy is dissipated in internal resistance.

• Concept of cool wires vs. hot wires:

  • For long-distance transmission we minimise losses by using low current, high voltage.

  • Low $I$ ⇒ lower $I^{2} R$ losses ⇒ wires stay cooler and less energy wasted.

  • Alternative (high I, low V) massively increases heating (poor choice).

• Microscopic view of heating: high current ⇒ more electron–ion collisions ⇒ increased lattice vibration ⇒ higher temperature.

Sample Worked Examples (from transcript)

• Energy transferred in 1 s by 2 A through 230 V:

  • $E = V I t = 230 \times 2 \times 1 = 460\,\text{J}$

• Power dissipated by 3 A through 10 Ω resistor:

  • Quick: $P = I^{2} R = 3^{2} \times 10 = 90\,\text{W}$ (matches $VI$ route).

• Electricity bill example (800 W toaster for 1 min):

  • $E = P t = 800\,\text{W} \times 60\,\text{s} = 4.8 \times 10^{4}\,\text{J}$

• 1.8 kW kettle for 5 min ⇒ energy in J & kWh:

  • Joules: $P=1.8\text{ kW}=1800\,\text{W};\; t=300\,\text{s} \Rightarrow E = 1800 \times 300 = 5.4 \times 10^{5}\,\text{J}$

  • kWh route: time = $\tfrac{5}{60} = 0.0833\,\text{h};\; E = 1.8\,\text{kW} \times 0.0833\,\text{h} \approx 0.15\,\text{kWh}$ (consistent with $\frac{5.4\times10^{5}}{3.6\times10^{6}}$).

• Series cells for 6 V using 1.5 V cells: need 4 cells in series (1.5 V × 4 = 6 V).

• Circuit with 20 Ω + 10 Ω in series, I = 0.4 A: total V = $IR = 0.4 \times 30 = 12\,\text{V}$.

Filament Lamp & Non-Ohmic Devices

• Filament lamp (tungsten)

  • Tungsten chosen for very high melting point (~3000 °C) ⇒ doesn’t melt when hot.

  • As filament warms, resistance increases, brightness rises then stabilises.

• I–V Characteristic (qualitative graph):

  • Curve starts steep then flattens (resembles elongated “S”).

  • Shows non-linear, non-Ohmic behaviour; resistance not constant.

  • Therefore Ohm’s law
    $\text{(constant }R\text{)}$ is not obeyed.

• Other non-Ohmic / variable-resistance components introduced in upcoming lessons: diodes, LEDs, LDRs, thermistors — all have distinctive I–V curves, none give straight lines.

Exam Guidance & Typical Marking Points

• Always quote a relevant formula when explaining proportionality (e.g. $P=I^{2}R$ for transmission loss Qs).

• For ‘why does wire heat’ questions include: electron flow → frequent collisions with ions → increased vibration & temperature → energy dissipated as heat.

• High-level structured questions (4–6 marks) often require:

  1. State relation (formula).

  2. Discuss proportional change (direct vs inverse).

  3. Consequence (heating, energy loss, brightness change, etc.).

  4. Practical conclusion (use high V/low I, variable resistance component, etc.).

• Remember distinctions:

  • Energy in J or kWh; Power in W.

  • EMF (source) vs measured terminal p.d. (load) differ due to internal resistance & dissipation.

Looking Ahead

• Upcoming lessons will extend to additional I–V curves (diode, LDR, thermistor) and start Chemistry: electrolysis, titrations.