Steady-State Direct Current Circuits — AP Physics C: Electricity and Magnetism
AP Physics C: Electricity and Magnetism · AP Physics C: E&M Unit 3: Electric Circuits · 14 min read
1. Fundamentals of Steady-State DC★★☆☆☆⏱ 3 min
Steady-state direct current (DC) circuits are circuits where the magnitude and direction of current in every branch is constant over time, with no build-up or depletion of charge at any point. By convention, we use conventional current (flow of positive charge) from high to low potential.
2. Equivalent Resistance for Series & Parallel★★☆☆☆⏱ 4 min
Equivalent resistance simplifies a complex network of resistors into a single equivalent value that behaves the same way as the original network when connected to a voltage source. The rules for series and parallel combinations are:
**Series**: Same current flows through each resistor, connected end-to-end. Equivalent resistance: $R_{\text{eq}} = \sum_{i=1}^n R_i$. Adding series resistors increases total resistance, like increasing conductor length.
**Parallel**: Each resistor connected across the same potential difference, forming separate branches. Equivalent resistance: $\frac{1}{R_{\text{eq}}} = \sum_{i=1}^n \frac{1}{R_i}$. Adding parallel resistors decreases total resistance, by adding more current paths.
Exam tip: Always simplify circuits starting from the innermost (furthest from the source terminals) combination and work back toward the terminals; starting from the source end often leads to misidentifying series vs parallel combinations.
3. Kirchhoff's Rules for Multi-Loop Circuits★★★☆☆⏱ 5 min
For circuits that cannot be reduced to a single equivalent resistance (e.g., multiple batteries in different branches), we use Kirchhoff's two rules, derived from fundamental conservation laws:
Exam tip: Never change your assumed current direction if you get a negative value. The negative sign already indicates direction opposite your assumption; changing directions mid-calculation almost always causes sign errors.
4. Emf, Terminal Voltage, and Power★★★☆☆⏱ 4 min
All real voltage sources have internal resistance from their constituent materials. Emf ($\varepsilon$) is the open-circuit potential difference across the source when no current is drawn. When current $I$ is drawn from a discharging source, terminal voltage (potential across the source terminals) is:
V = \varepsilon - Ir
Power dissipated by a resistor can be written three equivalent ways, and power supplied by a source is $P = \varepsilon I$. The maximum power transfer theorem states that power delivered to an external load resistor $R$ from a source with emf $\varepsilon$ and internal resistance $r$ is maximized when $R = r$, with maximum power:
P_{\text{max}} = \frac{\varepsilon^2}{4r}
Exam tip: When asked for power from a battery, clarify if the question asks for total power supplied by the source (includes power lost to internal resistance) or power delivered to the external load.
Common Pitfalls
Why: Rushing the final step; AP MCQ distractors are specifically designed to match this common error.
Why: Confusion between potential rise and drop, mixing up conventional and electron current direction.
Why: Confusing steady-state with transient charging/discharging where capacitors carry current.
Why: Confusing parallel and series battery combinations, where series emfs do add.
Why: Confusing potential drop direction when discharging vs charging.
Why: Not realizing charge conservation at the last junction is automatically implied by previous equations.