MCAT Chemical and Physical Foundations of Biological Systems Flashcards: 4c Resistors Capacitors Series Parallel

What this deck covers

This deck focuses on 4c Resistors Capacitors Series Parallel, giving you a quick way to review the definitions, rules, and examples that matter most for MCAT Chemical and Physical Foundations of Biological Systems.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is the current during capacitor discharging through $R$ starting from $V_0$?

Answer: $I(t)=\frac{V_0}{R}e^{-t/\tau}$. Discharging current begins at V₀/R and decreases exponentially as stored charge depletes.

Flashcard 2: In a parallel capacitor circuit, which quantity is the same across each capacitor: $Q$ or $V$?

Answer: Voltage $V$ is the same across all parallel capacitors. Parallel capacitors are connected across the same potential difference, equalizing voltage on each.

Flashcard 3: What is the equivalent capacitance relation for capacitors $C_1$ and $C_2$ in series?

Answer: $\frac{1}{C_{eq}}=\frac{1}{C_1}+\frac{1}{C_2}$. For series capacitors, reciprocals add since charges are equal and total voltage is the sum of individual voltages.

Flashcard 4: What is the current during capacitor charging in an RC circuit with battery $V$ and resistance $R$?

Answer: $I(t)=\frac{V}{R}e^{-t/\tau}$. Charging current starts at maximum V/R and decays exponentially as the capacitor voltage rises.

Flashcard 5: If $V_{tot}=12\ \text{V}$ across series resistors $2\ \Omega$ and $4\ \Omega$, what is $V$ across $4\ \Omega$?

Answer: $V=8\ \text{V}$. Voltage divides proportionally; the 4Ω resistor takes 4/6 of total voltage.

Flashcard 6: Find $C_{eq}$ for capacitors $2\ \mu\text{F}$ and $3\ \mu\text{F}$ in series.

Answer: $C_{eq}=\frac{6}{5}\ \mu\text{F}$. For two series capacitors, equivalent capacitance is their product divided by their sum.

Flashcard 7: What is the total charge relation for parallel capacitors in terms of capacitor charges $Q_i$?

Answer: $Q_{tot}=\sum Q_i$. With identical voltage, total charge on parallel capacitors sums the charges on each.

Flashcard 8: In a series resistor circuit, which quantity is the same through every resistor: $I$ or $V$?

Answer: Current $I$ is the same through all series resistors. In a series circuit, current has only one path, remaining constant through each resistor by conservation of charge.

Flashcard 9: If two series capacitors are $2\ \mu\text{F}$ and $4\ \mu\text{F}$ with charge $Q$, what is $\frac{V_{2\mu F}}{V_{4\mu F}}$?

Answer: $\frac{V_{2\mu F}}{V_{4\mu F}}=2$. With equal charge, voltage ratio is inverse to capacitance ratio, so V_{2μF} is twice V_{4μF}.

Flashcard 10: In a parallel resistor circuit, which quantity is the same across each branch: $I$ or $V$?

Answer: Voltage $V$ is the same across all parallel branches. Parallel branches connect across the same points, experiencing identical potential difference by definition.

Flashcard 11: Find $C_{eq}$ for capacitors $2\ \mu\text{F}$ and $3\ \mu\text{F}$ in parallel.

Answer: $C_{eq}=5\ \mu\text{F}$. Parallel capacitances sum directly to yield the equivalent capacitance.

Flashcard 12: What is the voltage division relation for series resistors: $V_i$ in terms of $R_i$ and $V_{tot}$?

Answer: $V_i=V_{tot}\frac{R_i}{\sum R}$. Voltage drops proportionally to each resistor's share of the total resistance in a series circuit.

Flashcard 13: Find $C_{eq}$ for two series capacitors $C$ and $C$ (identical capacitors).

Answer: $C_{eq}=\frac{C}{2}$. Two identical series capacitors sum reciprocals, yielding half the individual capacitance.

Flashcard 14: What is the equivalent resistance for resistors $R_1$ and $R_2$ in series?

Answer: $R_{eq}=R_1+R_2$. Resistances in series add directly as current flows through each sequentially, increasing total opposition to flow.

Flashcard 15: In a series capacitor circuit, which quantity is the same on each capacitor: $Q$ or $V$?

Answer: Charge $Q$ is the same on all series capacitors. Series capacitors share the same current, resulting in equal charge accumulation on each plate.

Flashcard 16: What is the charge division relation for series capacitors: $V_i$ in terms of $C_i$ and $Q$?

Answer: $V_i=\frac{Q}{C_i}$. With constant charge on series capacitors, voltage on each is inversely proportional to its capacitance.

Flashcard 17: Find $R_{eq}$ for resistors $2\ \Omega$ and $3\ \Omega$ in parallel.

Answer: $R_{eq}=\frac{6}{5}\ \Omega$. For two parallel resistors, equivalent resistance is their product divided by their sum.

Flashcard 18: Identify the correct discharging equation for a capacitor: $V_C(t)$ starting from $V_0$.

Answer: $V_C(t)=V_0e^{-t/\tau}$. During discharge, capacitor voltage decays exponentially from its initial value over time constant τ.

Flashcard 19: Find $R_{eq}$ for two parallel resistors $R$ and $R$ (identical resistors).

Answer: $R_{eq}=\frac{R}{2}$. Two identical parallel resistors double the conductance, halving the equivalent resistance.

Flashcard 20: Identify the correct charging equation for a capacitor: $V_C(t)$ in an RC circuit with battery $V$.

Answer: $V_C(t)=V\left(1-e^{-t/\tau}\right)$. Capacitor voltage approaches the battery voltage exponentially during charging in an RC circuit.

Flashcard 21: What is the RC time constant formula for a circuit with equivalent values $R_{eq}$ and $C_{eq}$?

Answer: $\tau=R_{eq}C_{eq}$. The time constant in RC circuits is the product of equivalent resistance and capacitance, governing exponential behavior.

Flashcard 22: What is the equivalent resistance relation for resistors $R_1$ and $R_2$ in parallel?

Answer: $\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}$. In parallel, conductances add, so the reciprocal of equivalent resistance equals the sum of reciprocals of individual resistances.

Flashcard 23: What is the equivalent capacitance for capacitors $C_1$ and $C_2$ in parallel?

Answer: $C_{eq}=C_1+C_2$. Capacitances in parallel add because they share the same voltage, and total charge is the sum of individual charges.

Flashcard 24: What is the total current relation for parallel resistors in terms of branch currents $I_i$?

Answer: $I_{tot}=\sum I_i$. By Kirchhoff's current law, total current entering a parallel junction equals the sum of branch currents.

Flashcard 25: Find $R_{eq}$ for resistors $2\ \Omega$ and $3\ \Omega$ in series.

Answer: $R_{eq}=5\ \Omega$. Series resistances add directly to give the total equivalent resistance.