Circuit Conqueror Summary Sheet
MCAT High-Yield Blueprint
CIRCUIT CONQUEROR
Comprehensive Summary Sheet: Electrostatics, Circuits & Magnetism
Name _________________
Target Date ____ / ____ / ____
1. Charge & Current
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Electric Circuit: Pathway for charge movement. Consists of voltage source, wires, and components.
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Current (\(I\)): Charge flow over time.
\(I = \frac{Q}{\Delta t}\) \(I\): Amperes (A = C/s), \(Q\): Coulombs (C)
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Conduction Electrons: Delocalized, free-moving electrons. Note: \(1\text{ C}\) & \(1\text{ A}\) are extremely large physical quantities.
MCAT High-Yield Constants
<table class="w-full text-[9px] text-slate-700"><tbody><tr class="border-b border-teal-100/50"><td class="py-0.5 font-semibold">Elementary Charge (\(e\))</td><td class="py-0.5 text-right font-mono">\(1.6 \times 10^{-19}\text{ C}\)</td></tr><tr class="border-b border-teal-100/50"><td class="py-0.5 font-semibold">Electron Charge</td><td class="py-0.5 text-right font-mono">\(-1.6 \times 10^{-19}\text{ C}\)</td></tr><tr><td class="py-0.5 font-semibold">Electron Volt (\(1\text{ eV}\))</td><td class="py-0.5 text-right font-mono">\(1.6 \times 10^{-19}\text{ J}\)</td></tr></tbody></table>
2. Potential, Fields, & Drift
Directional Dynamics
- • Negative charges naturally move opposite to electric field lines.
- • Electrons drift toward higher electric potential.
- • Drift direction is rightward if the E-field points left, or if the right end is at higher potential.
Charge Carriers
Any mobile particle carrying charge:
- • Metals: Delocalized electrons.
- • Semiconductors: Positive holes.
- • Solutions: Ions (e.g., salt water).
Theoretical Model vs. Physical Reality
Conventional Current
Flow of positive charges. Moves from (+) to (-) terminal (clockwise).
Electron Flow
Physical electron drift. Moves toward higher potential (+) terminal.
3. Ohm's Law
Current is directly proportional to voltage and inversely proportional to resistance.
\(V = I \times R\) Note: Only apply with 1 resistor or equivalent parts.
Ohm's Relationship Helper
V = I × R I = V / R R = V / I
Cover the value you want to solve for on the standard formula triangle.
4. Resistance & Resistivity
Resistance \(R\) depends on geometry. Materials are Ohmic if \(R\) remains constant as \(V\) is varied.
\(R = \rho \frac{L}{A}\)
\(\rho\): Resistivity (material property)
L: Length of conductor (\(R \propto L\))
A: Cross-sectional area (\(R \propto \frac{1}{A}\))
Area Relationship Area is proportional to the square of diameter (\(A \propto d^2\)). Doubling diameter decreases resistance by 4x.
Unit Definition Resistance unit: Volt per amp (\(\text{V/A}\)) or Ohm (\(\Omega\)). Same resistivity = same material.
5. Resistor Networks: Series vs. Parallel
| Parameter | Series (\(-\Box-\Box-\)) | Parallel (\(=\Box=\)) |
|---|
| Current (\(I\)) | Constant: \(I_{\text{tot}} = I_1 = I_2\) | Splits: \(I_{\text{tot}} = I_1 + I_2\) |
| Voltage Drop (\(V\)) | Splits: \(V_{\text{tot}} = V_1 + V_2\) | Constant: \(V_{\text{tot}} = V_1 = V_2\) |
| Equivalent \(R\) | \(R_{\text{eq}} = R_1 + R_2 + \dots\) | \(R_{\text{eq}} = \frac{R_1 R_2}{R_1 + R_2}\) (for 2) |
| Pathway | Charges pass through all | Charges pass through either, not both |
Conservation of Charge Rule: Current entering a parallel junction equals the sum of currents passing through each individual resistor.
High-Yield Worked Practice
\(10\,\Omega\) and \(20\,\Omega\) resistors are in series. If current through \(10\,\Omega\) is \(1\text{ A}\), what is the voltage drop across \(20\,\Omega\)?
Answer: 20 V
Current is constant in series (\(I_{20} = 1\text{ A}\)). Using Ohm's Law: \(V = I \times R = 1\text{ A} \times 20\,\Omega = 20\text{ V}\).
Lenny MCAT Review Series Page 1 of 2
MCAT High-Yield Blueprint
POWER, CAPACITANCE, & MAGNETS
High-Yield Formula Reference & Advanced Electromagnetism
Section II: Advanced Circuits
6. Power & Energy
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Power (\(P\)): Rate at which energy is converted. \(P = \frac{\Delta E}{\Delta t}\). Unit: Watt (\(\text{W = J/s}\)).
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Conservation of Energy: Total power dissipated by resistors must equal the total power supplied by the battery.
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Friction & Dissipation: When non-conservative factors convert energy to heat or sound:
\(E_{\text{initial}} + W_{\text{other}} = E_{\text{final}}\)
\(P = I V\)
\(P = I^2 R\)
\(P = \frac{V^2}{R}\)
⚠️ TRAP: For power of a single resistor, use the voltage drop across THAT resistor, NOT the entire battery's voltage!
7. Battery emf & Terminal Voltage
- emf (\(\text{V}_{\text{emf}}\)): Ideal voltage of battery when no current flows.
- Terminal Voltage (\(V_{\text{term}}\)): Actual voltage supplied to circuit when current is active.
- Internal Resistance (\(r_{\text{int}}\)): Internal heat loss reduces terminal voltage:
\(V_{\text{term}} = \text{emf} - I \times r_{\text{int}}\) Therefore, terminal voltage is less than emf during discharge.
Circuit Indicators
⊣⊢
• Longer line = positive terminal (higher potential).
• Ground represents potential Zero (0 V).
8. Capacitance & Dielectrics
Capacitors store electrical charge. Inserting a dielectric (\(\kappa > 1\)) always increases capacitance: \(C = \kappa C_0\).
CONNECTED Battery Attached
Voltage Constant
Charge Increases
Energy Increases
\(Q = C V\) (Since C increases, charge must increase).
DISCONNECTED Battery Detached
Charge Constant
Voltage Decreases
Energy Decreases
\(V = Q / C\) (Since C increases, voltage must drop).
9. Magnetism Fundamentals
- Field Line Direction: Point from North to South.
- Poles: The North pole wants to align with external fields; the South pole aligns opposite to external fields.
- ⚠️ MCAT Work-Energy Rule: The magnetic force (\(F_B = q v B \sin\theta\)) is always perpendicular to velocity (\(\vec{F}_B \perp \vec{v}\)). Therefore:
• Magnetic force never changes a particle's speed.
• Magnetic force does exactly ZERO work on the particle.
10. Instruments
- Galvanometers: Primarily measure current. Can also measure voltage since voltage and current are proportionally related.
- SI Units Checklist:
• Time is always in seconds.
• Charge is in coulombs.
• Work/Energy is in joules.
Master the fundamentals to beat traps!
Lenny MCAT Review Series Page 2 of 2
