Chapter 29 - Direct Current (DC) Circuits

• An emf device maintains a potential difference between its terminals, which we measure in volts.
• EMF Devices come in two major types: DC and AC.
• Wire rule: The voltage across a wire ($\Delta V_{wire}$) is near zero because of the wire's low resistance (due to $V =$$IR$).
• Resistor rule: Connecting a voltmeter in parallel across a resistor or lightbulb with the red (positive) lead on the low-potential side and the black (negative) lead on the high-potential side produces a negative potential difference.
• Switch rule: A closed switch behaves like a wire, and the voltage across it is equal to zero.
• (Ideal) emf rule - If the red (positive) lead is connected to the positive terminal and the black (negative) lead to the negative terminal, the voltage measured is positive and equals the terminal potential: $\Delta V =$$V_{red} - V_{black} =$$\Delta V_{terminal} =$$\epsilon$
• Real emf rule: Potential difference is equal to terminal potential subtracted by internal resistance: $\Delta V_{real} =$$\epsilon - Ir$
• Kirchhoff's loop rule: The total change in potential around any closed loop in a circuit is always zero.
• Resistors in series: $R_{eq} =$$R_1+$$R_2+$$R_3+$$...+$$R_N =$$\sum_{i=1}^NR_i$
• Resistors in parallel: $\frac{1}{R_{eq}} =$$\frac{1}{R_1} +$$\frac{1}{R_2} +$$\frac{1}{R_3} +$$... +$$\frac{1}{R_N} =$$\sum_{i=1}^N\frac{1}{R_N}$
• Current in a charging RC circuit: $I(t) =$$\frac{\epsilon}{R}e^{-t/RC}$
• Charge in a charging RC circuit: $q(t) =$$C\epsilon(1-e^{-t/RC})$
• Charge in a discharging RC circuit: $q(t) =$$q_{max}e^{-t/r}$
• Current in a discharging RC circuit: $I(t) =$$-I_{max}e^{-t/r}$
• Kirchoff's junction rule: At a junction, the sum of all currents entering a junction is equal to the sum of all currents leaving a junction.
• An RC circuit consists of an emf device, a resistor and a capacitor.
• The time constant ($\tau$) for a RC circuit is defined as $\tau \equiv RC$