Electricity: electrostatics, DC circuits, capacitors
Electricity: electrostatics, DC circuits, capacitors
This domain tests Coulomb's law, electric field and potential, DC circuits with resistors and internal resistance, Kirchhoff's rules, and capacitor behaviour in steady state and during charging. Expect numerical circuit problems and conceptual questions about field lines and equipotentials.
Core rules
- Coulomb and field: F=kq1q2/r² and E=F/q=kQ/r². Field lines point away from positive charge; equipotentials are perpendicular to field lines.
- Potential: V=kQ/r; potential difference is work per unit charge. For a uniform field, E=V/d.
- DC circuits: Ohm's law V=IR; series resistances add; parallel conductances add, so 1/R_p=Σ1/R_i. Kirchhoff's rules: junction currents sum to zero, and loop voltage changes sum to zero.
- Internal resistance: terminal voltage is V=ε−Ir. Maximum power transfer to a load occurs at R=r, but efficiency is then only 50%.
- Capacitors: C=Q/V; parallel capacitance adds, series reciprocal adds. Energy stored is U=½CV²=Q²/(2C). In DC steady state a capacitor draws no current.
- Dielectric: inserting a dielectric of constant κ multiplies C by κ if the capacitor is isolated with fixed Q, lowering V and U.
Worked example
A 12 V battery has internal resistance 1.0 Ω and is connected to 6.0 Ω and 3.0 Ω resistors in parallel. The parallel combination is R_p=(6×3)/(6+3)=2.0 Ω. Total resistance is 3.0 Ω, so I=12/3.0=4.0 A. Terminal voltage is V=12−4.0×1.0=8.0 V. The branch currents are 8.0/6.0=1.3 A and 8.0/3.0=2.7 A; they sum to 4.0 A. This shows that the terminal voltage, not the emf, drives the external circuit.
Traps
Assuming current is 'used up' around a series circuit; giving parallel branches different voltages; treating a capacitor as a short circuit in DC steady state; omitting internal resistance; mixing prefixes such as μC and mC; reversing the direction of E for a negative charge.