Conductors, Capacitors, and Dielectrics unit test

A test on this unit alone, marked as a percentage and a letter grade — for the test your class is actually sitting, rather than for May. Answer everything, then submit once: seeing the answer to question 3 before attempting question 4 makes the final percentage meaningless.

Paper 1 Paper 2 Paper 3

Each paper is built from this unit’s 19 terms and is the same for everyone, so a teacher can assign “Unit 3, Paper 1” and every student sits the identical test. Multiple choice is marked objectively; the written sections you mark yourself against the model answer and rubric.

Suggested time 37 min 34 points0/17 attempted

Energy stored in a capacitor

Capacitance definition

Parallel plate capacitance

Energy density of an electric field

Force between capacitor plates

Capacitors in series and parallel

Capacitor in a circuit at steady state

Partially filled dielectric

Charge redistribution between capacitors

Dielectric constant

RC circuit charging

Why energy changes when a dielectric is inserted

Short answer 1. Define or explain: General method for capacitance

3 pts

Short answer 2. Define or explain: Dielectric at constant charge vs constant voltage

3 pts

Short answer 3. Define or explain: Capacitance of a spherical capacitor

3 pts

Short answer 4. Define or explain: Time constant

3 pts

Free response

10 pts

MATHEMATICAL ROUTINES (Question 1, 10 points). An isolated, air-filled, charged capacitor consists of two conducting coaxial cylindrical shells of length L: the inner shell has radius R1 and the outer shell radius R2, with R2 ≪ L. The surface charge densities of the inner and outer shells are +σ1 and −σ2, and the absolute values of the total charges on the shells are equal. For B: a material of dielectric constant κ fills the region R1 < r < R2 of the isolated, charged capacitor.

A(i). Using Gauss’s law, derive an expression for the magnitude E of the electric field as a function of radial distance r for R1 < r < R2, in terms of R1, σ1, r, and physical constants, as appropriate.

A(ii). Derive an expression for the absolute value ΔV of the potential difference between the shells in terms of R1, R2, σ1, and physical constants, as appropriate.

A(iii). Describe the graph of E as a function of r from r = 0 to beyond the outer shell.

B. Derive an expression for the capacitance C with the dielectric inserted, in terms of L, R1, R2, κ, and physical constants, as appropriate.