Chapter 28: Direct-Current Circuits

• Emf: For a battery or other power source, the amount of amount of work done per unit charge to force a current through the circuit,

= dW/dq .

• Internal resistance: All batteries have a small internal resistance r, which can be treated as in series with the battery itself; This implies that the actual terminal voltage V is related to the battery emf by

V = – Ir . 

• Potential differences: Finding the potential difference V across an emf device or a resistor with a current I flowing through it, and across a capacitor with a charge Q on it, including the sign of V.
   
• Resistors in series: The resistance equivalent to R₁, R₂, ... in series is

R_eq = R₁ + R₂ + ...

• Resistors in parallel: The resistance equivalent to R₁, R₂, ... in parallel is obtained from

R_eq^–1 = R₁^–1 + R₂^–1 + ...

• Kirchhoff's laws: Statement and use of the loop rule and the junction rule.
   
• RC circuits: The time constant is τ = RC; What happens to the charge across a capacitor and the current through a resistor when the capacitor is being charged or discharged.
  Charging the capacitor: The voltage varies in time according to

V(t) = V₀ (1 – e^–t/RC) ;   similarly, for the charge,   q(t) = Q (1 – e^–t/RC) .

Discharging the capacitor: The voltage varies in time according to

V(t) = V₀ e^–t/RC .