Atlas MCAT Course
Physical Foundations → Electrostatics & Circuits
Electrostatics & Circuits
Fields, potential, and controlled flow.
01The idea
Electricity is not mysterious energy. It is force-mediated motion of charge under constraints.
| Fluids | Circuits |
|---|---|
| Pressure | Voltage |
| Flow rate | Current |
| Viscosity | Resistance |
Electricity mirrors fluids.
THREAD · Gradients and flow
02Build the model
ACharge: the source of electrical interaction
Charge comes in two types, positive and negative. Like charges repel; opposite charges attract. Charge is conserved, quantized, and measured in coulombs (C).
BCoulomb’s law: force between charges
Here q₁ and q₂ are the charges, r is their separation, and k is Coulomb’s constant. Larger charge gives a stronger force; greater distance gives a weaker force (inverse square). Force is vectorial; direction matters.
CElectric field: force per unit charge
Instead of tracking pairwise forces, define a field:
Units: N/C or V/m. The field describes the environment; charges respond to the field.
Fields point away from positive charges and toward negative charges. Field lines encode direction (tangent) and strength (density).
DElectric potential: energy perspective
Electric potential (voltage) is electric potential energy per unit charge:
Units: volts (V = J/C).
EPotential difference: what drives motion
Charges move because of potential differences, not because of “high voltage” alone.
Positive charges move toward lower potential; negative charges move toward higher potential.
Note the difference from fields: potential ∝ 1/r, while field ∝ 1/r².
FFrom electrostatics to circuits
Electrostatics explains stored energy. Circuits explain continuous charge flow.
Current (amperes, A = C/s) is how much charge passes a point per unit time.
GResistance: opposition to flow
Higher resistance gives less current for the same voltage; at the same voltage, current is set by resistance.
HPower in circuits
ISeries vs. parallel circuits
JCapacitors: energy storage
Capacitors store energy in electric fields and release it quickly. In circuits, capacitors combine in the opposite pattern from resistors — this is deliberate:
| Arrangement | Resistors | Capacitors |
|---|---|---|
| Series | R_eq = R₁ + R₂ | 1/C_eq = 1/C₁ + 1/C₂ |
| Parallel | 1/R_eq = 1/R₁ + 1/R₂ | C_eq = C₁ + C₂ |
KTime-dependent circuits (brief)
Charging and discharging capacitors involve exponential behavior, with a time constant:
This sets how fast circuits respond.
LConnecting to biology (context lock-in)
These principles explain neuronal membrane potentials, ion channel currents, cardiac conduction, and electrical signaling vs diffusion. Physics constrains physiology.
03See the connections
The lesson names these links itself. Read the map left to right.
Electrostatics
- Coulomb: 1/r²
- Field E (force)
- Potential V (energy), 1/r
Circuits
- V = IR
- P = IV
- Series vs parallel
Storage
- C = Q/V; U = ½CV²
- τ = RC
Next: thermodynamics.
04Reason with it
Four questions. Answer in your head first, then choose. You’ll see the reasoning either way.
Think first.
The distance between two charges doubles. What happens to the force between them?
Think first.
Which way does a positive charge move on its own?
Think first.
Two equal resistors are connected in parallel. What is the equivalent resistance?
Think first.
Two identical capacitors are connected in parallel. What is the total capacitance?
05MCAT lens
Equation-level checks
Field ∝ 1/r²; potential ∝ 1/r
Charges move because of potential differences
V = IR; P = IV = I²R = V²/R
Resistors add in series; capacitors add in parallel
τ = RC sets response speed
06Common traps
Trap 1: Field and potential fall off the same way
Misconception
Field ∝ 1/r²; potential ∝ 1/r.
Correct model
Fields give forces; potential gives energy.
Trap 2: High voltage alone makes charge move
Misconception
Charges move because of potential differences.
Correct model
ΔU = qΔV.
Trap 3: Capacitors combine like resistors
Misconception
They follow the opposite pattern.
Correct model
Capacitors add in parallel; resistors add in series.
07Dependency check
Can you reconstruct this concept without looking at the page? You should now be able to reason through:
Why charges interact
Check against 02 · A and B: Coulomb’s law.
Why fields and potentials are different
Check against 02 · C through E: force vs energy, 1/r² vs 1/r.
What drives current
Check against 02 · E and F: potential differences.
How resistance and capacitance control flow
Check against 02 · G through K.
If something feels unclear, the missing idea is usually thisElectricity is energy-driven charge motion under constraints.
08Remember
REMEMBER · if you keep only a few things
- Voltage ↔ pressure; current ↔ flow; resistance ↔ viscosity.
- F = kq₁q₂/r²; E = kq/r²; V = kq/r.
- Positive charges move toward lower potential.
- V = IR; P = IV.
- Resistors add in series; capacitors add in parallel.
- τ = RC.
09Forward hook
Electricity completes the charge layer. The last physics topic is energy accounting for gases.
How do heat, work, and internal energy trade off in a process?
That leads to thermodynamics and P–V diagrams.
Next lessonFluids, Pressure, and Flow→