Circuits

Physics and Math

Kinematics and Dynamics
Work and Energy
Thermodynamics
Fluids
Electrostatics and Magnetism
Circuits
Waves and Sound
Light and Optics
Atomic and Nuclear Phenomena
Mathematics
Reasoning About the Design and Execution of Research
Data-Based and Statistical Reasoning
High-Yield Cheat Sheet

Progress

Early access Want this book as a guided course? Placement diagnostics, interactive lessons, and checkpoints, built on these books.

Original study material © Premier Exam Prep — https://premierexamprep.com/mcat/books/physics-and-math/circuits · pep-wm-0bfb22d3

MCAT Books › Physics and Math › Circuits

Chapter 6: Circuits

3 min read Updated Mar 26, 2026

Read the entire chapter on one page Every section in order, with the sidebar tracking where you are as you scroll.

→

🎯 Diagnostic: Test Your Starting Level 24 questions (2 per section). No prior reading required, see what you already know.

Aim to answer every question before checking. Missed questions point you to the sections you need most.

1. (6.1) Electric current I is:

A) Voltage
B) The rate of flow of positive charge, I = dQ/dt (amperes, 1 A = 1 C/s)
C) Power
D) Resistance

B. Conventional current points in the direction positive charges would move (opposite the actual electron drift in metals).

2. (6.1) EMF (ε) of a battery is:

A) A resistive loss
B) Current through the battery
C) The energy per unit charge delivered by the source (volts); the potential difference when no current is flowing
D) Capacitance

C. EMF is NOT a force, despite the name; it is energy per charge.

3. (6.2) Ohm's law is:

A) I = P / V
B) R = P / I
C) V = I / R
D) V = I × R

D. Holds for ohmic conductors; non-ohmic elements (e.g., diodes) deviate.

4. (6.2) Resistance depends on:

A) Material (resistivity ρ), length (longer = more R), and cross-sectional area (thicker = less R), via R = ρL / A
B) Only on temperature
C) Only on voltage
D) Frequency alone

A. Temperature affects resistivity: metals heat up → R increases; semiconductors → R decreases.

5. (6.3) Resistors in series:

A) Share the same voltage
B) Carry the same current through each; total resistance is $R_{\text{total}}$ = R₁ + R₂ + ... (always greater than any individual)
C) Increase total current
D) Halve the current

B. Voltage divides across series resistors in proportion to R.

6. (6.3) In a series resistor combination:

A) Only the largest resistor matters
B) Total voltage equals the battery EMF
C) Total resistance is the sum ( $R_{\text{total}}$ = Σ $R_{i}$ ); voltage divides in proportion to each resistor's value
D) All currents are different

C. This is why voltage dividers work.

7. (6.4) Resistors in parallel:

A) Have the same current through each
B) Have different voltages across each
C) Only matter for DC
D) Share the same voltage; 1/ $R_{\text{total}}$ = Σ (1/ $R_{i}$ ); total R is smaller than any individual

D. More parallel paths mean more total current for a given voltage.

8. (6.4) Two 6 Ω resistors in parallel have total resistance:

A) 3 Ω (1/R = $\frac{1}{6}$ + $\frac{1}{6}$ = $\frac{1}{3}$ ⇒ R = 3)
B) 12 Ω
C) 6 Ω
D) 0 Ω

A. For N identical resistors R in parallel, total = R/N.

9. (6.5) Internal resistance of a battery:

A) Is zero
B) Causes the terminal voltage to be less than the EMF when current flows: $V_{\text{terminal}}$ = ε - I × $r_{\text{internal}}$
C) Only matters in parallel circuits
D) Is infinite

B. A near-dead battery has a high internal resistance, dropping its terminal voltage sharply under load.

10. (6.5) As a battery ages:

A) EMF rises
B) Terminal voltage rises
C) Internal resistance rises; for a given load, the terminal voltage drops more, reducing usable voltage
D) Current is independent of age

C. A fresh battery has

r_{\text{internal}}

~0.1 Ω; an exhausted one can have several ohms.

11. (6.6) Kirchhoff's junction rule states:

A) Sum of potentials around a closed loop is zero
B) Voltage multiplies
C) Resistance is additive
D) Sum of currents entering a node equals the sum of currents leaving it (charge conservation)

D. A direct consequence of charge conservation.

12. (6.6) Kirchhoff's loop rule states:

A) The sum of potential differences around any closed loop is zero (energy conservation)
B) Current is conserved at nodes only
C) Resistance × current = 0
D) EMF halves at each node

A. Goes around in a consistent direction: EMFs contribute positively if you traverse from - to +; resistors contribute negatively if current is in your direction of travel.

13. (6.7) Power dissipated in a resistor equals:

A) Only V × I
B) P = V × I = I² × R = V² / R (three equivalent forms for ohmic resistors)
C) V² × R
D) Q × T

B. Pick the form that uses the quantities you know most directly.

14. (6.7) A "60 W at 120 V" light bulb has resistance (at operating temperature):

A) 60 W at any voltage
B) 60 Ω
C) R = V² / P = 120² / 60 = 240 Ω
D) Infinite

C. Resistance of a tungsten bulb is much lower when cold; that's why filaments often burn out at turn-on.

15. (6.8) A capacitor stores:

A) Inductive energy
B) Current
C) Only voltage
D) Electric field energy, U = ½ C V², where C is capacitance and V is voltage across the plates

D. Equivalent forms: U = Q²/(2C) = ½QV.

16. (6.8) The capacitance of a parallel-plate capacitor in vacuum is:

A) C = ε₀ A / d, proportional to plate area and inversely proportional to plate separation
B) C = Q × V
C) C = V / Q
D) C = Q × d

A. Larger plates and thinner gaps give higher capacitance.

17. (6.9) Capacitors in parallel:

A) All have the same charge
B) Share the same voltage; total capacitance $C_{\text{total}}$ = C₁ + C₂ + ... (opposite of resistors)
C) Have different voltages
D) Combine as 1/ $C_{\text{total}}$

B. Acts like increasing the plate area.

18. (6.9) Capacitors in series:

A) Share the same voltage
B) Double the voltage
C) Share the same charge; 1/ $C_{\text{total}}$ = Σ(1/ $C_{i}$ ), so $C_{\text{total}}$ is smaller than any individual capacitance
D) Are not useful

C. Series acts like increasing the effective plate separation.

19. (6.10) A dielectric inserted between capacitor plates:

A) Decreases capacitance
B) Blocks all current permanently
C) Discharges the capacitor
D) Increases capacitance by a factor κ (dielectric constant): C = κ × ε₀ × A / d

D. Dielectrics also increase the maximum voltage before breakdown.

20. (6.10) The dielectric constant of water is:

A) About 80 (much higher than vacuum, κ = 1; air κ ≈ 1.0006; glass κ ≈ 5-10)
B) 1
C) 0
D) Negative

A. This is why water effectively "screens" ionic interactions (why salts dissolve so well).

21. (6.11) Conductivity σ is:

A) The same as resistance
B) The inverse of resistivity, σ = 1/ρ (units S/m); higher σ means less resistance to current flow
C) The reciprocal of capacitance
D) Always zero

B. Insulators have near-zero σ; metals have σ > 10⁷ S/m.

22. (6.11) An ammeter:

A) Measures voltage between two points
B) Measures capacitance
C) Measures current; is placed in SERIES with the component; ideally has zero internal resistance
D) Measures resistance

C. A voltmeter, by contrast, is placed in parallel and has very high (ideally infinite) internal resistance.

23. (6.12) The time constant of an RC circuit is:

A) τ = R / C
B) τ = R + C
C) τ = V / I
D) τ = R × C, and the capacitor charges to about 63% (or discharges by 63%) in one time constant

D. After 5τ, charging/discharging is essentially complete (>99%).

24. (6.12) In a charging RC circuit (capacitor initially uncharged, battery ε applied):

A) $V_{C}$ (t) = ε × (1 - e^(-t/RC)); capacitor voltage rises exponentially toward ε
B) Capacitor charges linearly
C) Current remains constant
D) Capacitor immediately reaches ε

A. Current, meanwhile, starts at ε/R and decays to zero as charging completes.

Previous Attempts

You flip a light switch and the room floods with light. The delay between flipping and seeing is so small your brain registers it as instant. But in that sliver of time, billions of electrons started drifting through copper wire, a potential difference pushed charge through a hot tungsten filament, and energy was converted from electrical to thermal to visible light.

All of that happened because of one thing: a complete circuit. Break the loop anywhere — burned-out switch, frayed wire, dead bulb — and everything stops.

Circuits are the backbone of every electronic device you interact with: phones, laptops, cars, defibrillators, MRI machines, the LED lights in your house. For the MCAT, circuits sit at the intersection of electrostatics (last chapter) and practical problem-solving. The good news: circuit physics on the MCAT is almost entirely algebra. No calculus, no complex AC analysis. If you can handle Ohm’s law and know how resistors and capacitors combine in series and parallel, you can tackle any circuit question the exam throws at you.

💡 Real World

A circuit is a water park. The battery is the pump that lifts water to the top of the slides (provides energy). The wires are the pipes connecting everything (low-resistance pathways). The resistors are the narrow, winding slides where water loses energy to friction. The rule: water the pump lifts up must eventually flow back down. No dead ends — the path has to form a complete loop, or nothing flows.

In This Chapter

6.1 Current and EMF
6.2 Resistance and Ohm’s Law
6.3 Resistors in Series
6.4 Resistors in Parallel
6.5 Internal Resistance
6.6 Kirchhoff’s Laws
6.7 Power in Circuits
6.8 Capacitors
6.9 Capacitors in Series and Parallel
6.10 Dielectrics
6.11 Conductivity and Meters
6.12 RC Circuits and Problem Solving
Section Test

← PreviousSection Test Next →Current and EMF

Scroll or pinch to zoom

Full chapter