ch 10

EMF & Terminal Voltage Flashcards

Front: What is electromotive force (emf), and is it actually a force?

Back: Despite its name, emf is not a force; it is a special type of potential difference. It represents the work done per unit charge ($\epsilon = \frac{dW}{dq}$) when no current is flowing.

Front: How does an emf source (like a battery) maintain a potential difference?

Back: It acts as a charge pump, using energy from chemical reactions to do work on negative charges, moving them from the positive terminal to the negative terminal to increase their potential energy.

Front: What defines an ideal battery?

Back: An ideal battery is an emf source that has no internal resistance. Its terminal voltage remains constant and equal to the emf, regardless of the current.

Front: What is terminal voltage ($V_{terminal}$), and how is it measured?

Back: It is the voltage measured across the actual terminals of a battery. In a real battery, it is calculated as:

Vterminal=ϵ−IrV_{terminal} = \epsilon - Ir

Front: Why does the terminal voltage of a real battery decrease as the current increases?

Back: Because of the potential drop ($Ir$) across the battery's internal resistance. As more current ($I$) flows, more voltage is "lost" inside the battery itself.

Front: What happens to internal resistance ($r$) as a battery is depleted?

Back: Internal resistance increases as the battery is used up, often due to oxidation of the plates or reduced acidity in the electrolyte.

Front: How do you calculate the current ($I$) through a circuit with a load resistor ($R$) and internal resistance ($r$)?

Back: The current is determined by the total resistance in the circuit:

I=ϵr+RI = \frac{\epsilon}{r + R}

Front: Why must a battery charger have a voltage output greater than the battery's emf?

Back: To reverse the normal direction of current. This makes the current ($I$) negative in the equation $V = \epsilon - Ir$, resulting in a terminal voltage greater than the emf to replenish chemical potential.

Front: In metallic wires, which direction do electrons flow compared to conventional current?

Back: Electrons flow in the opposite direction of conventional (positive) current flow—moving from the negative terminal, through the circuit, to the positive terminal.Flashcard 1: Basic Definitions

Front: What is the fundamental function of a resistor, and what equation governs its behavior?

Back: A resistor limits the flow of charge in a circuit. It is an ohmic device governed by Ohm’s Law:

V=IRV = IR

Flashcard 2: Equivalent Resistance

Front: What determines the equivalent resistance of a circuit containing multiple resistors?

Back: It depends on two factors:

  1. The individual values of the resistors.

  2. How they are connected (series, parallel, or a combination).

Flashcard 3: Series Circuit Characteristics

Front: What are the three major features of resistors connected in series?

Back: 1. Current: The same current flows through each resistor sequentially.

2. Resistance: The equivalent resistance is the algebraic sum of individual resistances ($R_S = R_1 + R_2 + ... + R_N$).

3. Voltage: The total source voltage is divided among the resistors; the sum of potential drops equals the source voltage.

Flashcard 4: Parallel Circuit Characteristics

Front: What are the three major features of resistors connected in parallel?

Back: 1. Voltage: The potential drop across each resistor is the same.

2. Current: The total current from the source is divided among the resistors; the sum of individual currents equals the total current ($\sum I_{in} = \sum I_{out}$).

3. Resistance: The equivalent resistance is found using reciprocals and is always less than the smallest individual resistance in the group.

Flashcard 5: Mathematical Formulas

Front: Compare the formulas for Equivalent Resistance ($R$ ) in Series vs. Parallel.

Back: * Series: $R_S = \sum_{i=1}^{N} R_i$

  • Parallel: $R_P = \left( \sum_{i=1}^{N} \frac{1}{R_i} \right)^{-1}$

Flashcard 6: Kirchhoff’s Junction Rule

Front: Based on the parallel circuit highlights, what is the Junction Rule?

Back: The sum of the currents flowing into a junction must be equal to the sum of the currents flowing out of the junction:

∑Iin=∑Iout\sum I_{in} = \sum I_{out}

Front: What is the definition of a junction (also known as a node)?

Back: A connection of three or more wires in a circuit.

Front: State Kirchhoff’s First Rule (The Junction Rule).

Back: The sum of all currents entering a junction must equal the sum of all currents leaving the junction:

∑Iin=∑Iout\sum I_{in} = \sum I_{out}

Front: What physical principle is the Junction Rule based on?

Back: The conservation of charge. Whatever charge flows into the junction must flow out.

Front: State Kirchhoff’s Second Rule (The Loop Rule).

Back: The algebraic sum of changes in potential around any closed circuit path (loop) must be zero:

∑V=0\sum V = 0

Front: What physical principle is the Loop Rule based on?

Back: The conservation of energy. In a closed loop, energy supplied by a voltage source must be transferred into other forms by the devices in that loop.

Problem-Solving & Sign Conventions

Front: When moving across a resistor in the same direction as the current flow, how do you treat the potential change?

Back: You subtract the potential drop ($-IR$).

Front: When moving across a resistor in the opposite direction of the current flow, how do you treat the potential change?

Back: You add the potential drop ($+IR$).

Front: How do you treat the potential change when moving across a voltage source from the negative terminal to the positive terminal?

Back: You add the potential drop ($+V$).

Front: How do you treat the potential change when moving across a voltage source from the positive terminal to the negative terminal?

Back: You subtract the potential drop ($-V$).

Foundations & Charging

Front: What is the definition of an RC circuit?

Back: An electrical circuit containing a combination of resistance (R) and capacitance (C). The capacitor stores energy in an electric field, while the resistor governs the rate at which charge flows.

Front: What happens to the charge ($q$) on a capacitor as time ($t$) approaches infinity during the charging process?

Back: The exponential term $e^{-t/\tau}$ approaches zero, and the charge reaches its maximum value:

Q=CεQ = C\varepsilon

Front: Define the time constant ($\tau$) and its physical units.

Back: The time constant is defined as:

τ=RC\tau = RC

It is measured in seconds. It represents the time required to charge a capacitor to approximately 63.2% of its maximum capacity (or discharge it to 36.8%).

Front: Describe the behavior of current ($I$) in a circuit as a capacitor charges.

Back: Current is at its maximum ($I_0 = \varepsilon/R$) at $t = 0$ and decreases exponentially toward zero as the capacitor reaches full charge. The formula is:

I(t)=I0e−t/τI(t) = I_0 e^{-t/\tau}

Discharging & Dynamics

Front: When a switch is moved to the discharge position, what happens to the voltage source?

Back: The voltage source is removed from the circuit, and the circuit reduces to a simple series connection where the capacitor's stored charge flows through the resistor.

Front: What is the formula for the charge on a capacitor as a function of time during discharge?

Back: The charge decreases exponentially from the initial charge ($Q$):

q(t)=Qe−t/τq(t) = Qe^{-t/\tau}

Front: What does the negative sign in the discharging current formula ($I(t) = -\frac{Q}{RC} e^{-t/\tau}$) signify?

Back: It indicates that the current flows in the opposite direction of the current produced during the charging process.