Chapter 4 Problems
Original chapter problems, with explicitly stated assumptions and authored solutions. These retain the manuscript’s problem identities; calculus extensions and unfinished material make no AP coverage claim.
Original problem 1
An ideal 12 V source is connected across C₁=2 μF in series with a parallel pair C₂=C₃=3 μF. All capacitors start uncharged. Find the equivalent capacitance.
Authored clarification: The original refers to “blah” without a recoverable named circuit. This is an explicitly authored replacement with a complete stated topology and values; no original diagram or source answer is inferred.
Worked solution with reasons for each step · Original reading location
Archived original prompt
No original chapter-problem answer was supplied. This worked solution is authored for the explicitly stated reviewed prompt.
Original problem 2
An ideal 12 V source is connected across C₁=2 μF in series with a parallel pair C₂=C₃=3 μF. All capacitors start uncharged. At electrostatic equilibrium, find the voltage across each capacitor.
Authored clarification: The original refers to “blah” without a recoverable named circuit. This is an explicitly authored replacement with a complete stated topology and values; no original diagram or source answer is inferred.
Worked solution with reasons for each step · Original reading location
Archived original prompt
No original chapter-problem answer was supplied. This worked solution is authored for the explicitly stated reviewed prompt.
Original problem 3
An ideal 12 V source drives R₁=4 Ω in series with a parallel pair R₂=6 Ω and R₃=3 Ω. Find the equivalent resistance.
Authored clarification: The original refers to “blah” without a recoverable named circuit. This is an explicitly authored replacement with a complete stated topology and values; no original diagram or source answer is inferred.
Worked solution with reasons for each step · Original reading location
Archived original prompt
No original chapter-problem answer was supplied. This worked solution is authored for the explicitly stated reviewed prompt.
Original problem 4
An ideal 12 V source drives R₁=4 Ω in series with a parallel pair R₂=6 Ω and R₃=3 Ω. Find each resistor current.
Authored clarification: The original refers to “blah” without a recoverable named circuit. This is an explicitly authored replacement with a complete stated topology and values; no original diagram or source answer is inferred.
Worked solution with reasons for each step · Original reading location
Archived original prompt
No original chapter-problem answer was supplied. This worked solution is authored for the explicitly stated reviewed prompt.
Original problem 5
Optional RC supplement: arbitrary-time exponential formulas. Prerequisites: exponentials and the time constant τ=RC; the optional calculus derivation also uses logarithms and derivatives. This item makes no AP coverage claim.
An ideal single-loop RC circuit has R=2.00 kΩ and C=100 μF, so τ=RC=0.200 s. At t=0 an uncharged capacitor is connected to a 12 V ideal source. Find q(t).
Authored clarification: The original refers to “blah” without a recoverable named circuit. This is an explicitly authored replacement with a complete stated topology and values; no original diagram or source answer is inferred.
Worked solution with reasons for each step · Original reading location
Archived original prompt
No original chapter-problem answer was supplied. This worked solution is authored for the explicitly stated reviewed prompt.
Original problem 6
Optional RC supplement: arbitrary-time exponential formulas. Prerequisites: exponentials and the time constant τ=RC; the optional calculus derivation also uses logarithms and derivatives. This item makes no AP coverage claim.
An ideal single-loop RC circuit has R=2.00 kΩ and C=100 μF, so τ=RC=0.200 s. A capacitor initially at 12 V is disconnected from its source and discharged through R at t=0. Find q(t).
Authored clarification: The original refers to “blah” without a recoverable named circuit. This is an explicitly authored replacement with a complete stated topology and values; no original diagram or source answer is inferred.
Worked solution with reasons for each step · Original reading location
Archived original prompt
No original chapter-problem answer was supplied. This worked solution is authored for the explicitly stated reviewed prompt.
Original problem 7
Optional RC supplement: arbitrary-time exponential formulas. Prerequisites: exponentials and the time constant τ=RC; the optional calculus derivation also uses logarithms and derivatives. This item makes no AP coverage claim.
An ideal single-loop RC circuit has R=2.00 kΩ and C=100 μF, so τ=RC=0.200 s. The initially uncharged capacitor begins charging from a 12 V ideal source. Find the source current I(t), positive toward the capacitor’s positive plate.
Authored clarification: The original refers to “blah” without a recoverable named circuit. This is an explicitly authored replacement with a complete stated topology and values; no original diagram or source answer is inferred.
Worked solution with reasons for each step · Original reading location
Archived original prompt
No original chapter-problem answer was supplied. This worked solution is authored for the explicitly stated reviewed prompt.
Original problem 8
Optional RC supplement: arbitrary-time exponential formulas. Prerequisites: exponentials and the time constant τ=RC; the optional calculus derivation also uses logarithms and derivatives. This item makes no AP coverage claim.
An ideal single-loop RC circuit has R=2.00 kΩ and C=100 μF, so τ=RC=0.200 s. The source is removed and a capacitor initially at 12 V discharges through R. Find the current magnitude I_out(t) flowing out of its positive plate as a function of time for t≥0, with time measured from source removal at t=0.
Authored clarification: The original refers to “blah” without a recoverable named circuit. This is an explicitly authored replacement with a complete stated topology and values; no original diagram or source answer is inferred.
Worked solution with reasons for each step · Original reading location
Archived original prompt
No original chapter-problem answer was supplied. This worked solution is authored for the explicitly stated reviewed prompt.