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

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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.

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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 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 2: 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 3: 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 4: 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 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: 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 8: 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 9: 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.

Flashcard 10: 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 11: 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 12: 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 13: 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 14: 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 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: 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 17: 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 18: 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 19: 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 20: 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 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: 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 23: 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 24: 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 25: 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.