AP Unit 11 Problems

Construct the current-versus-time graph and find the charge-flow magnitude through a cross section and the number of electrons involved over the full 9.0 s.

Give the electron drift direction, explain why current is not added as a spatial vector at a bend, and describe electron motion during the zero-current interval.

Compare their currents and the charge each transfers in the next 2.0 s if its current remains constant. Explain why emf should have units of volts rather than newtons.

At the same current, a wire is bent into a U shape without adding branches. Compare current through its two legs and state the relation of electron drift to current arrows.

Draw the U-shaped wire and add conventional-current and electron-drift arrows on both legs.

Draw the circuit with conventional-current arrows and standard symbols. Identify two complete loops and the component belonging to both. Show how to mark an adjustable resistor.

Predict branch behavior when the switch opens. Does the resistor branch also stop? Can the open switch have nonzero voltage?

Draw the changed topology, including the retained feed resistor. Explain and calculate the load voltage and current and the source current after the shunt is added. Relate the result to the definition of a short.

Consider a separate hypothetical circuit: remove both finite resistors and connect the ideal 12 V source directly to only ideal zero-resistance wire. Why is there no sensible finite steady current? State what real effects must be restored. Explain why changing only a line’s bend differs from adding the shunt in part a.

Derive RB/RA. For ρ = 2.0 × 10⁻⁸ Ω·m, L = 1.0 m, and a = 0.10 mm, calculate each resistance and describe the distinction between R and ρ.

Wire A is heated while its geometry changes negligibly. Predict its typical metallic resistance trend and explain why an ideal constant-resistivity ohmic calculation might give a different prediction.

Plot I versus ΔV for both elements. Determine the fixed element’s resistance and whether each data set supports one constant-R model over the tested range. Explain how changing graph axes alters the slope interpretation.

Design a check for heating as the cause of the bulb’s changing resistance. Identify measured variables, a temperature-related control, a repeat procedure, and where the thermal energy comes from. Contrast this with the ideal fixed-ρ model.

Derive the resistor forms of power from P = IΔV, then find current, power, and converted energy.

Compare power if source voltage doubles with R fixed, and if resistance doubles with source voltage fixed. Create two qualitative graphs: P versus positive V with R fixed, and P versus positive R with V fixed. Label axes and explain each shape.

Connect them in series. Find each power, rank brightness, and explain the fixed-current comparison.

Reconnect them in parallel across 12 V. Find each power, rank brightness, and explain why the ranking reverses. State a limitation for real bulbs.

With the added branch open, find equivalent resistance, source current, branch currents, and voltage drops. Explain the topology behind each equality.

First draw and label the node schematic and branch-current arrows.

Close the extra 12 Ω branch. Predict and calculate the new equivalent resistance, source current, and original 6 Ω branch current. Why does original branch current change here even though the battery is ideal?

Find current, loaded terminal voltage, load voltage, and open-circuit terminal voltage. Explain when wire resistance may be neglected and why it is retained here.

Draw and label the complete connected meter schematic: an ammeter to measure load current and a voltmeter to measure load voltage. State ideal meter resistances and qualitatively discuss nonideal meter effects.

Find emf and both resistances, construct the signed loop equation, and explain how the graph tests energy conservation.

For 0.50 C passing through this loop, give the source energy input and conversion in each resistor. Create a quantitative potential-versus-position graph with labeled components and voltage scale if the starting reference becomes 0 V.

A student writes 15 − 2I0 − 3I1 − 6I2 = 0 as a single-loop equation. Explain the path error, write two independent correct loops and one junction equation, and solve the three currents.

Draw and label the source, feed, both return branches and the three assumed current directions before writing equations.

Write the loop going down the 3 Ω branch and up the 6 Ω branch. Is it independent? Create a labeled qualitative potential-versus-ordered-position graph through the source, feed, and 6 Ω return branch with source negative terminal set to zero; mark the calculated plateau potentials.

Find ID and the charge leaving through D in 5.0 s. State the conservation principle used.

If a student instead reports ID = 0.80 A outward, find the predicted accumulation rate in the junction region and explain why this is inconsistent with steady conditions.

Solve the signed current in D and redraw its actual direction. Compare both incoming and outgoing totals after correction.

Find current through both series resistors in B. Explain why neither the bend angle nor the first resistor’s heating reduces the second resistor’s current.

For the series connection, derive Ceq, find each charge and voltage, and explain why equal charge magnitude follows from conservation. Compare Ceq to the smaller capacitor.

Reconnect the uncharged capacitors in parallel across 12 V. Find Ceq and each plate-charge magnitude, and explain how the equivalent represents the source’s total charge separation.

Find the charging time constant and initial and long-time values of current, capacitor voltage, charge, and stored energy. Explain the initial wire and final open-branch models.

Sketch charging Q, VC, current magnitude, and energy against time, indicating endpoint behavior and the meaning of one τ. Compare qualitatively if R doubles with all else fixed. Do not use a transient formula.

After it is fully charged, switch to discharge. State initial current direction and magnitude, describe immediate and long-time changes in charge and energy, and explain the 37% landmark.

Create labeled qualitative discharge graphs of Q, VC, current magnitude and stored energy against time, showing their starting values and zero asymptotes.

Design a coherent measurement procedure to collect the current–voltage data: identify the connected meters, varied and measured quantities, temperature and geometry controls, repeated readings, and a test of constant R. Then infer resistance and a range from the supplied slope bounds and calculate resistivity.

At the stated 4.0 V operating point, find power and charge transferred in 30 s. Find converted energy two ways and explain why heating can change later readings.

Draw the node schematic and write two independent junction equations and three independent loop equations. Explain why the left pair and right pair cannot be treated as simple series groups before solving.

Solve the branch currents and node potentials VB and VC. Verify one unused loop and the source-power balance.

Where would ideal meters measure bridge current and VB − VC? Describe qualitatively how a finite-resistance voltmeter across B–C could disturb the bridge.

Draw the two meter connections on the bridge schematic.

For the initial charging instant and long-time charging state, find VB, currents through R1 and R2 and C, final capacitor charge, and final energy. Explain why long-time capacitor voltage is not 12 V.

Draw the initial wire-equivalent and long-time open-branch equivalent schematics, keeping R2 connected in both.

After disconnecting the source and R1, find the discharge time constant and initial current magnitude through R2. Sketch VC and current magnitude during discharge. State initial stored energy and the total energy eventually converted in R2.

Plan a hands-on check of the discharge time constant without exponential fitting. Name measured variables, controls, repetitions, and sampling uncertainty. A sample trial gives (t in s, VC in V): (0,8.0), (0.20,4.9), (0.30,3.8), (0.40,3.0), (0.50,2.3), (0.60,1.8), (0.80,1.1). Each voltage has uncertainty ±0.1 V and each sample time ±0.02 s. Create a quantitative plot of VC/VC,0 versus time with scales and uncertainty; read an approximate τ from the 37% landmark and explain its precision.