MCAT Chemical and Physical Foundations of Biological Systems Flashcards: 4c Electric Potential Voltage Capacitance

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This deck focuses on 4c Electric Potential Voltage Capacitance, 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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Flashcard 1: How does inserting a dielectric with constant $\kappa$ change parallel-plate capacitance?

Answer: $C=\kappa\frac{\varepsilon_0A}{d}$. Dielectric insertion reduces the effective field, increasing capacitance by the factor $\kappa$.

Flashcard 2: What is the SI unit of capacitance?

Answer: $1\ \text{F}=1\ \text{C/V}$. The farad measures capacitance as one coulomb of charge stored per volt of potential difference.

Flashcard 3: State the relation between electric field and electric potential in one dimension.

Answer: $E=-\frac{dV}{dx}$. The electric field is the negative rate of change of potential with respect to position.

Flashcard 4: If $V(r)=\frac{kQ}{r}$, what is the ratio $\frac{V(2r)}{V(r)}$?

Answer: $\frac{V(2r)}{V(r)}=\frac{1}{2}$. Potential inversely proportional to distance, so doubling $r$ halves the potential.

Flashcard 5: Find $Q$ stored on a capacitor with $C=5\ \mu\text{F}$ and $V=12\ \text{V}$.

Answer: $Q=CV=60\ \mu\text{C}$. Charge stored is the product of capacitance and applied voltage.

Flashcard 6: Identify $C_{\text{eq}}$ for two identical capacitors $C$ in series.

Answer: $C_{\text{eq}}=\frac{C}{2}$. For identical capacitors in series, equivalent is half due to doubled effective separation.

Flashcard 7: State the formula for potential difference between two points in terms of work.

Answer: $\Delta V=-\frac{W_{\text{field}}}{q}$. Potential difference equals the negative work done by the field per unit charge when moving a charge between points.

Flashcard 8: Which has zero work by the electric field: motion along or perpendicular to an equipotential surface?

Answer: Perpendicular motion has $W=0$ (along equipotential). Motion perpendicular to the field lines follows equipotential surfaces, resulting in no change in potential and zero work.

Flashcard 9: What is the electric potential energy of two point charges $q_1$ and $q_2$ separated by $r$?

Answer: $U=\frac{kq_1q_2}{r}$. Represents the work to assemble the charges from infinity, analogous to gravitational potential energy.

Flashcard 10: What is the definition of electric potential $V$ at a point?

Answer: $V=\frac{U}{q}$ (electric potential energy per unit charge). Electric potential at a point is the electric potential energy per unit charge for a test charge placed there.

Flashcard 11: What is the SI unit of electric potential (voltage)?

Answer: $1\ \text{V}=1\ \text{J/C}$. The volt is defined as the potential difference that imparts one joule of energy to one coulomb of charge.

Flashcard 12: What is the definition of capacitance $C$ in terms of charge and voltage?

Answer: $C=\frac{Q}{\Delta V}$. Capacitance quantifies the ability to store charge for a given potential difference across the device.

Flashcard 13: State the energy stored in a capacitor in terms of $Q$ and $C$.

Answer: $U=\frac{Q^2}{2C}$. Alternative form obtained by substituting $Q=CV$ into the energy expression.

Flashcard 14: What is the superposition rule for electric potential from multiple charges?

Answer: $V_{\text{net}}=\sum_i \frac{kQ_i}{r_i}$. Electric potential is a scalar quantity, allowing direct summation of individual contributions.

Flashcard 15: State the equivalent capacitance for capacitors in series.

Answer: $\frac{1}{C_{\text{eq}}}=\sum_i \frac{1}{C_i}$. In series, total voltage divides across capacitors, leading to reciprocal sum for equivalent capacitance.

Flashcard 16: State the equivalent capacitance for capacitors in parallel.

Answer: $C_{\text{eq}}=\sum_i C_i$. In parallel, charges add while sharing the same voltage, summing individual capacitances.

Flashcard 17: Identify $C_{\text{eq}}$ for two identical capacitors $C$ in parallel.

Answer: $C_{\text{eq}}=2C$. Parallel connection doubles effective plate area for identical capacitors, doubling capacitance.

Flashcard 18: State the relationship between change in electric potential energy and voltage.

Answer: $\Delta U=q\Delta V$. Change in potential energy equals charge times the potential difference experienced by the charge.

Flashcard 19: Which quantity is continuous across a conductor's surface in electrostatic equilibrium: $V$ or $E$?

Answer: $V$ is constant throughout the conductor. In electrostatic equilibrium, the potential is uniform inside and on the surface of a conductor due to zero internal field.

Flashcard 20: What is the electric potential due to a point charge $Q$ at distance $r$?

Answer: $V=\frac{kQ}{r}$. Derived from integrating the electric field from infinity to $r$, assuming zero potential at infinity.

Flashcard 21: State the energy stored in a capacitor in terms of $C$ and $V$.

Answer: $U=\frac{1}{2}CV^2$. Energy stored derives from the work to charge the capacitor, integrating $Q dV$ from 0 to $V$.

Flashcard 22: In a uniform electric field, what is the relation between $\Delta V$, $E$, and displacement $\Delta x$ along the field?

Answer: $\Delta V=-E\Delta x$. In a uniform field, potential decreases linearly in the direction of the field by the product of field strength and distance.

Flashcard 23: State the capacitance of a parallel-plate capacitor with plate area $A$ and separation $d$ (vacuum).

Answer: $C=\frac{\varepsilon_0A}{d}$. For parallel plates, capacitance increases with area and decreases with separation, proportional to permittivity.

Flashcard 24: Find the energy stored when $C=2\ \mu\text{F}$ and $V=3\ \text{V}$.

Answer: $U=\frac{1}{2}CV^2=9\ \mu\text{J}$. Energy calculation uses the formula derived from integrating work done during charging.

Flashcard 25: What is the sign of $V$ at a point due to a negative source charge $Q<0$?

Answer: $V<0$. For $Q<0$, potential is negative relative to zero at infinity, indicating attractive interaction for positive test charges.