Electricity & DC Circuits
Current, voltage, resistance, Kirchhoff's laws and potential dividers
Current (I) = rate of flow of charge. I = Q/t (amperes). Conventional current flows from + to −.
Potential difference (V) = energy transferred per unit charge. V = W/Q (volts).
Resistance (R)** = V/I (ohms). **Ohm's Law: V ∝ I at constant temperature (for ohmic conductors).
Resistivity: R = ρL/A where ρ = resistivity, L = length, A = cross-sectional area.
Kirchhoff's Laws:
EMF (ε)** = total energy per unit charge from a source. **Internal resistance (r): ε = V + Ir → V = ε − Ir (terminal pd drops under load).
Potential divider: Two resistors in series: Vout = Vin × R₂/(R₁ + R₂). Used with thermistors (temperature sensing) and LDRs (light sensing) for automatic systems.
Key Points to Remember
- 1I = Q/t, V = W/Q, R = V/I
- 2Kirchhoff's laws: charge conservation + energy conservation
- 3EMF and internal resistance: ε = V + Ir
- 4Potential divider: Vout = Vin × R₂/(R₁+R₂)
Pakistan Example
Load Shedding and Internal Resistance — Pakistan's Grid Challenge
When WAPDA's generators supply heavy load, terminal voltage drops due to internal resistance (V = ε − Ir). This is why voltage drops during peak hours in Pakistan. Understanding Kirchhoff's laws helps engineers design the national grid — the 500 kV transmission network uses potential dividers (step-down transformers) to deliver safe 220V to homes.