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Flashcards · AP® Physics 2: Algebra-Based · Unit 11

Unit 11: Electric Circuits flashcards

53 cards on topics 11.1 to 11.8. Pick a topic or study the whole unit.

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11.1 Electric Current

What is electric current?
The rate at which charge passes through a cross-section of a conductor: I = ΔQ/Δt, in amperes (1 A = 1 C/s). It is measured at a place, not stored in a component.
What is the direction of conventional current?
The direction positive charge would move: from + to − outside the source. In metals, electrons carry the current and drift the opposite way.
What is emf?
The potential difference a source provides, ℰ, in volts. It is energy per unit charge, not a force. The source supplies energy; the charge carriers are already in the wire.
How do you find the charge that passes when the current changes?
Find the area under the I–t graph (A × s = C). Peak current × time overestimates it.
About how many electrons carry 1.0 C of charge?
N = ΔQ/e = 1.0 / (1.60 × 10⁻¹⁹) ≈ 6.25 × 10¹⁸ electrons.
How do electrons move in a wire carrying a current?
They already move randomly at about 10⁶ m/s with zero net motion. A potential difference adds a slow drift in one direction, and only the drift carries net charge.
Is current used up in a component?
No. The same current enters and leaves a component; energy is transferred, not charge.

11.2 Simple Circuits

What is a closed circuit, an open circuit and a short circuit?
Closed: a complete loop with a source, so charges can flow. Open: a break anywhere, so no current anywhere in that loop. Short: a path with no change in potential across an element, which then carries no current.
How are ideal ammeters and voltmeters connected?
An ammeter goes in the loop, so the current passes through it, and acts like a plain wire. A voltmeter goes across an element, one lead on each end, and lets no charge through.
A plain wire is connected across one of two bulbs in a single loop. What happens to that bulb?
It goes out. It is short-circuited: there is no potential difference across it, so no current through it.
A battery is connected to two bulbs, each in its own branch. How many closed loops are there?
Three: the battery with each bulb, and the loop through the two bulbs alone. Count loops without the battery too.
Does wire length or position on a schematic matter?
No. Schematics show connections only, and ideal wires have no change in potential along them. Crossing wires without a dot are not connected.
What happens when a switch in a single loop is opened?
There is no current anywhere in that loop, not just after the gap. Every element in the loop goes off.

11.3 Resistance, Resistivity, and Ohm’s Law

What is resistance, and how is it defined?
How strongly an object opposes the movement of charge: R = ΔV/I, in ohms (1 Ω = 1 V/A).
What is the difference between resistance and resistivity?
Resistivity ρ (Ω·m) is a property of the material. Resistance R = ρL/A is a property of one object and also depends on its length and cross-sectional area.
A wire is replaced by one of the same metal with three times the length and twice the diameter. How does R change?
Length × 3 gives R × 3. Diameter × 2 gives area × 4, so R ÷ 4. Overall R × 3/4.
What does the slope of an I against ΔV graph tell you?
Slope = 1/R, so a steeper line means a smaller resistance. A slope of 0.050 A/V gives R = 20 Ω.
What is an ohmic element?
One whose resistance is the same at every current, so I ∝ ΔV: its I–ΔV graph is a straight line through the origin. A curved graph through the origin is not ohmic.
Why does a filament bulb's resistance rise as it glows?
Its temperature rises, and the resistivity of most conductors increases with temperature: hotter atoms vibrate more and obstruct drifting electrons more often.
How do you find resistivity from lab data?
Measure R for different lengths of the same wire and plot R against L. The slope is ρ/A, so ρ = slope × A, with A = π(d/2)² in m².

11.4 Electric Power

What is electric power in a circuit element?
P = IΔV, energy per charge times charge per second, in watts (1 W = 1 J/s). It applies to every element.
When do you use P = I²R and when P = ΔV²/R?
P = I²R when elements share the same current (one loop): larger R, more power. P = ΔV²/R when they share the same ΔV (each across the same battery): smaller R, more power.
The potential difference across a resistor doubles. What happens to its power?
It multiplies by 4, since P = ΔV²/R at constant R. Tripling ΔV gives 9 times the power.
Two bulbs share one loop. Which is brighter?
The one with the larger resistance. They carry the same current, so P = I²R is bigger for the larger R. Brightness increases with power.
How much energy does a 60 W lamp transfer in 5.0 minutes?
ΔE = PΔt = 60 × 300 = 1.8 × 10⁴ J. Convert minutes to seconds.
Does a bulb's power rating apply in every circuit?
No. A rating such as "6.0 V, 3.0 W" applies only at the stated potential difference. A 12 W bulb can be dimmer than a 3 W bulb in some circuits.
How is energy balanced in a circuit with an ideal battery?
Energy supplied per second by the battery (Iℰ) equals the energy dissipated per second by resistors and bulbs, plus any being stored in a capacitor.

11.5 Compound Direct Current (DC) Circuits

How do you combine resistors in series and parallel?
Series: R_eq = R₁ + R₂ + … Parallel: 1/R_eq = 1/R₁ + 1/R₂ + …, then invert at the end. n identical resistors in parallel give R/n.
What is the equivalent resistance of 12 Ω and 6.0 Ω in parallel?
1/R_eq = 1/12 + 1/6.0 = 3/12, so R_eq = 4.0 Ω, less than either resistor.
What is shared in series and in parallel?
Series: the same current in each element (only one path). Parallel: the same potential difference across each branch (both ends on the same two points).
What is the terminal voltage of a real battery?
ΔV_terminal = ℰ − Ir, where r is the internal resistance. With one external resistance, I = ℰ/(R + r). The emf equals the terminal voltage only when there is no current.
A third bulb is added in parallel with two bulbs across an ideal battery. Does the first bulb get dimmer?
No. Its potential difference is still the emf, so its current and power are unchanged; the battery supplies more total current.
Why does a real voltmeter read slightly low?
It has very large but finite resistance. In parallel it lowers the resistance of that part of the circuit, so the potential difference there falls slightly.
A cell of emf 1.5 V and internal resistance 0.20 Ω carries 0.50 A. What is its terminal voltage?
ΔV = ℰ − Ir = 1.5 − 0.50 × 0.20 = 1.4 V.

11.6 Kirchhoff’s Loop Rule

What is Kirchhoff's loop rule?
The sum of potential differences round any closed loop is zero: ΣΔV = 0. Each point has one potential, so it is energy conservation for charges.
What are the sign rules for a loop equation?
Battery crossed − to +: +ℰ; + to −: −ℰ. Resistor crossed with the current: −IR; against it: +IR. Keep one direction round the loop.
A 1.5 V ideal cell drives a current through two resistors in series. One has 0.90 V across it. What is across the other?
1.5 − 0.90 = 0.60 V, by the loop rule.
Does the loop rule apply to loops with no battery?
Yes, to every closed loop. A loop through two parallel branches shows that they have equal potential differences.
In a single loop, what decides each resistor's share of the voltage?
Its resistance, not its position. With the same current, ΔV = IR is largest across the largest resistance.
How much electric potential energy does 3.0 C lose passing through a resistor with 4.0 V across it?
ΔU = qΔV = 3.0 × 4.0 = 12 J, converted to thermal energy in the resistor.

11.7 Kirchhoff’s Junction Rule

What is Kirchhoff's junction rule?
The total current into a junction equals the total current out: ΣI_in = ΣI_out. It follows from conservation of charge.
At a junction, 4.0 A enters along one wire and 2.5 A leaves along a second. What does the third wire carry?
1.5 A, leaving the junction, so that 4.0 A in = 2.5 + 1.5 A out.
How does current split between parallel branches?
Each branch has the same ΔV, so I = ΔV/R: more current through the smaller resistance. Split equally only for identical branches.
An ideal 6.0 V battery is across 4.0 Ω and 12 Ω in parallel. What are the currents?
6.0/4.0 = 1.5 A and 6.0/12 = 0.50 A; the battery carries 1.5 + 0.50 = 2.0 A.
Which conservation laws are behind Kirchhoff's two rules?
The junction rule is conservation of charge. The loop rule is conservation of energy. Most branched circuits need both.
What does a negative answer for a current mean?
The current flows opposite to the arrow you drew. Keep the sign; your choice of arrow was arbitrary.

11.8 Resistor-Capacitor (RC) Circuits

How do you combine capacitors in series and parallel?
Parallel: C_eq = C₁ + C₂ + … Series: 1/C_eq = 1/C₁ + 1/C₂ + … These are the reverse of the resistor rules. 3.0 μF and 6.0 μF give 2.0 μF in series and 9.0 μF in parallel.
What is shared by series capacitors?
The same charge Q, because the isolated inner plates keep zero net charge. Their ΔV values add, so the smallest capacitor has the largest ΔV.
How does an uncharged capacitor behave just after the switch closes and after a long time?
Just after closing it acts like a wire (ΔV_C = 0) and its branch current is largest. After many time constants it acts like a break, with zero current.
What is the time constant of an RC circuit?
τ = RC, in seconds (Ω × F = s). 10 kΩ and 100 μF give τ = 1.0 s. It depends only on R and C, not on the emf.
How do current and charge change while a capacitor charges through a resistor?
The current starts at ℰ/R and falls towards zero; Q, ΔV_C and stored energy rise towards their final values. Changes are fast at first, then slower.
Roughly how charged is a capacitor after one time constant?
About 63% of its final value, not full. Charging from 12 V, ΔV_C is about 7.6 V after one τ.
What happens when a charged capacitor discharges through a resistor?
Q, ΔV_C, current and stored energy all fall towards zero, fast at first then slower. The current in the capacitor's branch is reversed compared with charging.

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