#AP Physics 2: Electric Circuits - The Night Before ⚡

Hey there, future physics whiz! Let's get you prepped for the AP Physics 2 exam with a super-focused review of electric circuits. We'll make sure you're not just memorizing, but understanding the flow of electricity. Let's do this!

#Electric Charge and Current

# Definition and Conservation of Electric Charge

Electric charge is the fundamental property that makes matter interact with electromagnetic fields. Think of it as the 'stuff' that feels electrical forces. 💡

• Conservation of Charge: The total charge in a closed system never changes. It can move around, but the overall amount stays the same. This is a cornerstone of circuit analysis. It's like having a fixed amount of water in a closed system; you can move it around, but you can't create or destroy it.

• Charge Carriers: In most circuits, electrons are the primary charge carriers (though we use conventional current which assumes positive charge flow). This is a convention, but it makes everything consistent with electric field direction.

  

  Image: A visual representation of charge conservation in a circuit.

# Current 💨

Current (I) is the rate at which charge flows. It's like measuring how much water flows through a hose per second. The equation is:

$$I = \frac{\Delta Q}{\Delta t}$$

where:

• I is current (Amps, A or milliAmps, mA)
• ΔQ is the charge (Coulombs, C)
• Δt is the time (seconds, s)

• Conventional Current: We use the direction that a positive charge would move, even though electrons (negative) are actually moving. This is just a convention that aligns with electric field direction.

#Drift Velocity

• Drift Velocity (vd): This is the average velocity of charge carriers (usually electrons) in a wire due to an electric field. It's typically very slow (think mm/s), despite the speed of the electric field itself being close to the speed of light. It's like a crowd of people moving slowly in a direction, not individuals running fast.

• Factors affecting drift velocity: Electric field strength, charge, and mass of the particle

  

  Image: Illustration of electron drift velocity in a wire.

• Microscopic Current Equation: The current can also be expressed in terms of drift velocity:

  $$I = nqAv_d$$

  Where:

  • n is the number density of charge carriers
  • q is the charge of each carrier
  • A is the cross-sectional area of the wire
  • vd is the drift velocity

Example Problem:

A metal wire has a cross-sectional area of 1 square millimeter and is subjected to an electric field of 1000 volts per meter. The wire is made of a metal with a drift velocity of 1 millimeter per second for electrons. Calculate the electric current flowing through the wire.

Solution:

To solve this question, you would need to use the formula for electric current, which is I = nqAvd, where I is the electric current, q is the electric charge of the charged particles (in this case, electrons), A is the cross-sectional area of the wire, and vd is the drift velocity of the charged particles. Using the given values, the electric current flowing through the wire would be:

I = (1.6 x 10^-19 C) * (1 mm^2) * (1 mm/s) = 1.6 x 10^-19 C/s = 1.6 x 10^-15 A

Note that the electric current is very small because the drift velocity of the electrons is very small and the electric charge of an electron is also very small.

#Circuit Components and Measurement

# Circuit Symbols & Measuring Tools 🛠️

Here are some common circuit symbols. Knowing these is essential for drawing and interpreting circuit diagrams.

Image: Common circuit symbols, including a battery, resistor, capacitor, and switch.

#Measuring Tools

• Ammeter: Measures current (Amps). It's connected in series with the component you're measuring. Think of it as a device that counts the charge passing through it.

• Voltmeter: Measures potential difference (Voltage). It's connected in parallel across the component you're measuring. Think of it as measuring the 'push' on the charge between two points.

• Internal Resistance: Ammeters have very low internal resistance, so they don't impede the current. Voltmeters have very high internal resistance, so they don't draw significant current from the circuit.

# Final Exam Focus 🎯

#High-Priority Topics:

• Conservation of Charge: Understand how charge is conserved in circuits. It's a fundamental principle.
• Current and Drift Velocity: Know the relationship between current, charge, drift velocity, and wire properties.
• Circuit Symbols and Measurement: Be comfortable with circuit diagrams and how ammeters and voltmeters are used.

#Common Question Types:

• Conceptual Questions: Understanding the relationship between current, charge, and drift velocity.
• Circuit Analysis: Analyzing simple circuits with resistors and batteries.
• Measurement Questions: Knowing how to correctly use ammeters and voltmeters.

#Last-Minute Tips:

• Time Management: Don't get bogged down on one question. Move on and come back if you have time.
• Units: Always include units in your calculations and answers. It's an easy way to lose points if you forget.
• Draw Diagrams: If a question involves a circuit, draw a diagram to help you visualize it.
• Show Your Work: Even if you don't get the right answer, you can get partial credit for showing your work.

# Practice Questions 📝

Practice Question

#Multiple Choice Questions

1. A wire carries a current of 2 A. How much charge passes through a cross-section of the wire in 10 seconds? (A) 0.2 C (B) 5 C (C) 20 C (D) 100 C

2. Which of the following is true about the drift velocity of electrons in a wire? (A) It is equal to the speed of light. (B) It is very large compared to the speed of light. (C) It is typically very small (mm/s). (D) It is zero when no current is flowing.

3. An ammeter should be connected in a circuit in which way, and why? (A) Parallel, so it does not affect the current in the circuit. (B) Series, so it does not affect the current in the circuit. (C) Parallel, so it can measure the voltage drop. (D) Series, so it can measure the current flow.

#Free Response Question

A circuit consists of a battery with a voltage of 12 V and two resistors, R1 = 10 Ω and R2 = 20 Ω, connected in series.

(a) Draw a diagram of the circuit, including an ammeter to measure the current through R1 and a voltmeter to measure the voltage across R2. (2 points)

(b) Calculate the total resistance of the circuit. (2 points)

(c) Calculate the current flowing through the circuit. (2 points)

(d) Calculate the voltage drop across resistor R1. (2 points)

(e) Calculate the power dissipated by resistor R2. (2 points)

Scoring Breakdown:

(a) Circuit Diagram (2 points)

• 1 point for correct series circuit with battery and two resistors.
• 1 point for correct placement of ammeter (in series with R1) and voltmeter (in parallel with R2).

(b) Total Resistance (2 points)

• 1 point for correct use of series resistance formula: R_total = R1 + R2
• 1 point for correct calculation: R_total = 10 Ω + 20 Ω = 30 Ω

(c) Current (2 points)

• 1 point for correct use of Ohm's Law: I = V / R
• 1 point for correct calculation: I = 12 V / 30 Ω = 0.4 A

(d) Voltage Drop across R1 (2 points)

• 1 point for correct use of Ohm's Law: V1 = I * R1
• 1 point for correct calculation: V1 = 0.4 A * 10 Ω = 4 V

(e) Power Dissipated by R2 (2 points)

• 1 point for correct use of power formula: P = I^2 * R or P = V^2 / R or P=IV
• 1 point for correct calculation: P = (0.4 A)^2 * 20 Ω = 3.2 W or P=(8V)^2/20 = 3.2 W or P = 0.4*8 = 3.2 W

You've got this! Go ace that exam! 💪