--- title: "AP Physics C: E&M Experimental Design FRQ Practice" description: "41 Experimental Design and Analysis questions written in the AP format, each scored part by part." canonical: "https://fiveable.me/ap-physics-c-e-m/frqs/experimental-design" type: "frq-type-practice" subject: "AP Physics C: E&M" --- # AP Physics C: E&M Experimental Design FRQ Practice ## What the Experimental Design FRQ asks The Experimental Design and Analysis question is FRQ 3 on the AP Physics C: E&M exam. You plan a lab to find an electrical or magnetic quantity, explain how to graph the data, then graph a data table and use a best-fit line to calculate the value. - **25–30 min**: suggested on the exam - **10 points**: across parts A to D - **95 min**: for all four FRQs | Part | What it asks | Points | | --- | --- | --- | | A: Procedure | Describe how to collect data with the equipment provided | 2 | | B: Analysis plan | Describe what to graph and how the graph gives the quantity | 2 | | C: Graph | Choose two quantities, graph the data table, and draw a best-fit line | 4 | | D: Experimental value | Calculate the quantity from your best-fit line | 2 | ## How Experimental Design FRQ practice works 1. **Read the setup and data.** The lab scenario, the equipment, the data table, and parts A through D, laid out the way the exam shows them. 2. **Write on a 27-minute timer.** Inside the 25 to 30 minutes the exam suggests for this question. Pause it or turn it off, and your response saves as you go. 3. **Submit for a score out of 10.** Your response is scored against the scoring guidelines written for that question. Your first score is included. ## All 41 questions ### Unit 8: Electric Charges, Fields, and Gauss's Law (5) - [Dielectric permittivity measurement and analysis](/ap-physics-c-e-m/frq-practice?id=6977d54af7509ad45460c5f0&type=frq-3-experimental-design) - [Electric field magnitude around charged conducting sphere](/ap-physics-c-e-m/frq-practice?id=698abe214eb20800e3085127&type=frq-3-experimental-design) - [Dielectric permittivity from capacitor force measurements](/ap-physics-c-e-m/frq-practice?id=698ac4234eb20800e3085153&type=frq-3-experimental-design) - [Dielectric permittivity from capacitor measurements](/ap-physics-c-e-m/frq-practice?id=698acbdf4eb20800e308517f&type=frq-3-experimental-design) - [Dielectric permittivity determination using capacitor measurements](/ap-physics-c-e-m/frq-practice?id=698accd84eb20800e3085186&type=frq-3-experimental-design) ### Unit 9: Electric Potential (5) - [Electric field determination from potential measurements](/ap-physics-c-e-m/frq-practice?id=6977cccd6d7ee03370aa0a4f&type=frq-3-experimental-design) - [Dielectric permittivity measurement in parallel-plate capacitor](/ap-physics-c-e-m/frq-practice?id=698abd2d4eb20800e308511e&type=frq-3-experimental-design) - [Electric potential mapping between charged electrodes](/ap-physics-c-e-m/frq-practice?id=698ac0934eb20800e308513c&type=frq-3-experimental-design) - [Electric potential distribution between conducting electrodes](/ap-physics-c-e-m/frq-practice?id=698ac3f94eb20800e3085151&type=frq-3-experimental-design) - [Electric potential from charged conducting sphere](/ap-physics-c-e-m/frq-practice?id=698ac78c4eb20800e3085163&type=frq-3-experimental-design) ### Unit 10: Conductors and Capacitors (5) - [Electric field change with dielectric insertion](/ap-physics-c-e-m/frq-practice?id=698ac0534eb20800e3085139&type=frq-3-experimental-design) - [Dielectric permittivity determination using capacitor voltage measurements](/ap-physics-c-e-m/frq-practice?id=698ac5274eb20800e3085158&type=frq-3-experimental-design) - [Dielectric permittivity determination using capacitor measurements](/ap-physics-c-e-m/frq-practice?id=698acaeb4eb20800e3085178&type=frq-3-experimental-design) - [Dielectric constant effects on capacitor capacitance](/ap-physics-c-e-m/frq-practice?id=698acfa34eb20800e3085194&type=frq-3-experimental-design) - [Conducting slab insertion effects on capacitor capacitance](/ap-physics-c-e-m/frq-practice?id=6a95b4be0f2747638df7d8ae&type=frq-3-experimental-design) ### Unit 11: Electric Circuits (7) - [Capacitance determination through resistance variation](/ap-physics-c-e-m/frq-practice?id=6978015b6ba4e57abd6c3941&type=frq-3-experimental-design) - [Battery emf and internal resistance determination](/ap-physics-c-e-m/frq-practice?id=698ac1654eb20800e308513f&type=frq-3-experimental-design) - [Battery internal resistance and emf determination](/ap-physics-c-e-m/frq-practice?id=698ac30e4eb20800e308514c&type=frq-3-experimental-design) - [Internal resistance determination through terminal voltage measurement](/ap-physics-c-e-m/frq-practice?id=698ac6364eb20800e308515e&type=frq-3-experimental-design) - [Dielectric permittivity measurement via capacitance](/ap-physics-c-e-m/frq-practice?id=698ac73f4eb20800e3085162&type=frq-3-experimental-design) - [Battery internal resistance determination via wire length variation](/ap-physics-c-e-m/frq-practice?id=698ac8254eb20800e3085167&type=frq-3-experimental-design) - [Battery terminal voltage and internal resistance determination](/ap-physics-c-e-m/frq-practice?id=698acc3c4eb20800e3085182&type=frq-3-experimental-design) ### Unit 12: Magnetic Fields and Electromagnetism (15) - [Magnetic field dependence on current and core material](/ap-physics-c-e-m/frq-practice?id=698abe464eb20800e3085129&type=frq-3-experimental-design) - [Magnetic permeability determination through solenoid field measurement](/ap-physics-c-e-m/frq-practice?id=698abf3d4eb20800e3085133&type=frq-3-experimental-design) - [Magnetic permeability measurement via solenoid field variation](/ap-physics-c-e-m/frq-practice?id=698ac0784eb20800e308513b&type=frq-3-experimental-design) - [Magnetic permeability determination using solenoid core materials](/ap-physics-c-e-m/frq-practice?id=698ac1784eb20800e3085141&type=frq-3-experimental-design) - [Magnetic field enhancement in solenoids with core materials](/ap-physics-c-e-m/frq-practice?id=698ac3304eb20800e308514d&type=frq-3-experimental-design) - [Magnetic permeability determination in solenoids](/ap-physics-c-e-m/frq-practice?id=698ac41d4eb20800e3085152&type=frq-3-experimental-design) - [Magnetic permeability determination using solenoid core](/ap-physics-c-e-m/frq-practice?id=698ac5084eb20800e3085157&type=frq-3-experimental-design) - [Magnetic permeability determination using solenoid cores](/ap-physics-c-e-m/frq-practice?id=698ac6004eb20800e308515c&type=frq-3-experimental-design) - [Magnetic permeability determination in solenoid cores](/ap-physics-c-e-m/frq-practice?id=698ac7e34eb20800e3085164&type=frq-3-experimental-design) - [Magnetic permeability determination using solenoid measurements](/ap-physics-c-e-m/frq-practice?id=698ac8d34eb20800e308516a&type=frq-3-experimental-design) - [Magnetic permeability measurement via solenoid core testing](/ap-physics-c-e-m/frq-practice?id=698ac9af4eb20800e3085170&type=frq-3-experimental-design) - [Magnetic field variation with solenoid core materials](/ap-physics-c-e-m/frq-practice?id=698aca954eb20800e3085174&type=frq-3-experimental-design) - [Magnetic permeability determination using solenoid cores](/ap-physics-c-e-m/frq-practice?id=698acb8c4eb20800e308517d&type=frq-3-experimental-design) - [Magnetic permeability determination using solenoid measurements](/ap-physics-c-e-m/frq-practice?id=698acc8a4eb20800e3085183&type=frq-3-experimental-design) - [Magnetic permeability determination using solenoid measurements](/ap-physics-c-e-m/frq-practice?id=698ace8e4eb20800e3085191&type=frq-3-experimental-design) ### Unit 13: Electromagnetic Induction (4) - [Magnetic field magnitude from induced voltage measurements](/ap-physics-c-e-m/frq-practice?id=698aca5b4eb20800e3085173&type=frq-3-experimental-design) - [Electromagnetic induction, magnetic flux, experimental data analysis](/ap-physics-c-e-m/frq-practice?id=698acdec4eb20800e308518d&type=frq-3-experimental-design) - [Current growth in RL circuits with inductance determination](/ap-physics-c-e-m/frq-practice?id=6a8f9a5368a1bcf021dee200&type=frq-3-experimental-design) - [Series RLC circuit resonance and inductance determination](/ap-physics-c-e-m/frq-practice?id=6ab29c1dd21387d09448b29d&type=frq-3-experimental-design) ## Sample question **Dielectric permittivity measurement and analysis** A student is asked to determine the electric permittivity of an unknown dielectric material by measuring the electric field between two oppositely charged parallel conducting plates separated by a fixed distance. Part A (2 points): Prompt: **Describe** a procedure for collecting data that would allow the student to determine the relative permittivity κ of the dielectric slab. Your procedure should include (i) what quantities will be measured and how each will be measured using the available equipment, and (ii) at least one specific method for reducing experimental uncertainty (for example, multiple trials and averaging or systematic variation of an independent variable). Verb: describe Part B (2 points): Prompt: **Describe** how the collected data could be graphed and how that graph would be analyzed to determine κ. In your description, include a mathematical expression that relates the graph's slope (or slopes) to κ. Assume the electric field magnitude between the plates is E = V/d in air and E = V/(κd) when the dielectric fills the space. Verb: describe Figure 1: Type: apparatus_diagram Caption: Figure 1. Parallel-plate apparatus with sphere URL: https://kcbwzropdukwhmmvdylp.supabase.co/storage/v1/object/public/frq_stimulus/ap-physics-c-e-m/3ea45e63-bcfa-4366-a586-4e64b10b1ef7_fig1.jpg Placement: before-part Part Letter: C Figure 2: Type: modified_setup Caption: Figure 2. Apparatus with dielectric slab URL: https://kcbwzropdukwhmmvdylp.supabase.co/storage/v1/object/public/frq_stimulus/ap-physics-c-e-m/3ea45e63-bcfa-4366-a586-4e64b10b1ef7_fig2.jpg Placement: before-part Part Letter: C Figure 3: Type: blank_grid Caption: Figure 3. Blank grid for graphing URL: https://kcbwzropdukwhmmvdylp.supabase.co/storage/v1/object/public/frq_stimulus/ap-physics-c-e-m/3ea45e63-bcfa-4366-a586-4e64b10b1ef7_fig3.jpg Placement: before-part Part Letter: C Data Table for Part C: Headers: V (V) | θ_air (deg) | θ_d (deg) 100 | 7.1 | 5.2 200 | 14.0 | 10.4 300 | 20.5 | 15.6 400 | 26.3 | 20.6 500 | 31.6 | 25.5 Part C (4 points): Context: The student performs trials both with air between the plates and with the dielectric slab inserted as shown in Figure 2. For each applied potential difference V, the student measures the equilibrium angle θ of the suspended charged sphere relative to the vertical. The plate separation is d = 0.020 m and the sphere's mass is m = 0.0150 kg. The measured angles are shown in Table 1. i. **Indicate** two quantities, either measured quantities from Table 1 or additional calculated quantities, that could be graphed to produce a straight line that could be used to determine κ. Vertical axis: ______ Horizontal axis: ______ (1 pt) Verb: indicate ii. On the grid provided in Figure 3, create a graph of the quantities indicated in part C(i). - Use Table 2 to record the measured or calculated quantities that you will plot. - Clearly label the axes, including units as appropriate. - Plot the points you recorded in Table 2. (2 pt) Verb: create iii. **Draw** a best-fit line for the data graphed in part C(ii). (1 pt) Verb: draw Part D (2 points): Prompt: Using the best-fit line that you drew in part C(iii), **calculate** an experimental value for the relative permittivity κ of the dielectric slab. In your calculation, determine the slope using two points on your best-fit line and use a mathematical relationship that connects that slope to κ. Verb: calculate Image URLs (3): - https://kcbwzropdukwhmmvdylp.supabase.co/storage/v1/object/public/frq_stimulus/ap-physics-c-e-m/3ea45e63-bcfa-4366-a586-4e64b10b1ef7_fig1.jpg - https://kcbwzropdukwhmmvdylp.supabase.co/storage/v1/object/public/frq_stimulus/ap-physics-c-e-m/3ea45e63-bcfa-4366-a586-4e64b10b1ef7_fig2.jpg - https://kcbwzropdukwhmmvdylp.supabase.co/storage/v1/object/public/frq_stimulus/ap-physics-c-e-m/3ea45e63-bcfa-4366-a586-4e64b10b1ef7_fig3.jpg ## Questions **How many responses can I get scored?** You can read every question without a plan. Your first scored response is included. A plan unlocks unlimited scoring. **Do I need to have done the lab before?** No. The question describes the setup and the equipment you can use, and gives you a data table to graph in part C. **What should I plot?** Two quantities that give a straight line, so the slope or intercept leads to the value you need. Part C asks you to name them before you graph. **How do I make the graph?** Use the drawing tool to plot the data on the grid and draw a best-fit line. You can also graph on paper, switch to handwrite, and add a photo of your page. **Are these real College Board questions?** No. We wrote them in the AP format, with the same four parts, and wrote scoring guidelines for each one. ## Related - [Experimental Design FRQ exam guide](/ap-physics-c-e-m/ap-physics-c-electricity-magnetism-exam/ap-physics-c-e-m-frq-experimental-design/study-guide/ap-physics-c-e-m-frq-experimental-design) - [AP Physics C: E&M Mathematical Routines FRQ practice](/ap-physics-c-e-m/frqs/mathematical-routines) - [AP Physics C: E&M Representations FRQ practice](/ap-physics-c-e-m/frqs/translation-between-representations) - [AP Physics C: E&M Qualitative/Quantitative FRQ practice](/ap-physics-c-e-m/frqs/qualitative-quantitative-translation) - [AP Physics C: E&M FRQs](/ap-physics-c-e-m/frqs) - Any question by id: the `get_frq` tool on the [Fiveable MCP server](/mcp/docs) ## About This Document Canonical Fiveable pages are available as Markdown at the same path plus `.md`. - [llms.txt](https://fiveable.me/llms.txt): index of Fiveable's sections and URL patterns - [llms-full.txt](https://fiveable.me/llms-full.txt): complete subject and unit listing - [MCP server](https://fiveable.me/mcp): call Fiveable as tools instead of fetching pages (`https://fiveable.me/api/mcp`) - [MCP server for AP teachers](https://fiveable.me/mcp/teachers): a teacher's classes, assignments and AP-rubric grading (`https://fiveable.me/api/mcp/teacher`)