IP Physics Notes (Upper Secondary, Year 3-4): 11) Current of Electricity

Quick recap — Electric current measures how quickly charge moves. Define the energy supplied (emf) and used (p.d.), then apply Ohm's law, resistivity relations, and characteristic curves to decode circuit behaviour.

Charge & Current

• Charge \( Q \) measured in coulombs; \( 1 \) electron carries \( -1.6 \times 10^{-19} \pu{C} \).
• Current is rate of charge flow: \[ I = \frac{\Delta Q}{\Delta t} \]
• Conventional current: positive to negative. Electron flow: negative to positive.
• Total charge moved: \( Q = I t \).

Electromotive Force vs Potential Difference

• Emf \( \mathcal{E} \): work done by source per coulomb round the entire circuit, \( \mathcal{E} = \dfrac{W_\text{source}}{Q} \).
• Potential difference \( V \): work done per coulomb across a component, \( V = \dfrac{W_\text{component}}{Q} \).
• Both measured in volts; emf describes supply, p.d. describes energy drop in loads.

Resistance & Ohm's Law

• Resistance opposes current flow: \[ R = \frac{V}{I} \]
• Ohmic conductor: \( V \propto I \) at constant temperature.
• Resistivity relation for uniform wires: \[ R = \rho \frac{L}{A} \]
  • \( \rho \) material property (( \pu{\Omega.m} )), \( L \) length, \( A \) cross-sectional area.
• Temperature effects: metallic resistance increases with temperature; semiconductors often show opposite trend.

Worked Example: Calculating Resistivity

A copper wire (\( \rho = \pu{1.7 \times 10^{-8} \Omega.m} \)) is \( \pu{0.80 m} \) long with diameter \( \pu{0.90 mm} \). Area \( A = \pi (0.90 \times 10^{-3} / 2)^2 \) so \( R = \rho L / A \approx 2.7 \times 10^{-2} \space \Omega \).

I-V Characteristics to Memorise

• Gradient on \( V \)-against-\( I \) graph equals resistance; on \( I \)-vs-\( V \), resistance is reciprocal of gradient.

Practical Measurement Tips

• Ammeter in series (assume negligible resistance); voltmeter in parallel (assume infinite resistance).
• For accurate resistivity experiments, keep wire at constant temperature, measure length precisely, and average diameter readings with a micrometer.

Key Takeaways

• Use \( Q = I t \) to connect time, current, and charge.
• Differentiate supply emf from component p.d.; both share volt units but describe distinct energy transfers.
• Resistivity links microscopic material properties to macroscopic resistance; temperature shifts can explain non-linear graphs.
• Recognise signature I-V curves under exam pressure: straight line (ohmic), curved (filament), threshold (diode).