3.4 Direct Current & Circuits

Irodov Problems 3.147 to 3.218.

72problems
126figures
Difficulty2.2avgDifficulty: 8 rated 1, 45 rated 2, 18 rated 3, 1 rated 4, 0 rated 5; mean 2.2.
Uniqueness2.9avgUniqueness: 2 rated 1, 16 rated 2, 42 rated 3, 9 rated 4, 3 rated 5; mean 2.9.

No.	Title	Difficulty	Uniqueness	Methods
3.147	A Current Without Any Wire	Difficulty 1 of 5	Uniqueness 2 of 5	gauss law · current density
3.148	Water Rising Through a Capacitor	Difficulty 2 of 5	Uniqueness 3 of 5	capacitance · capacitor networks · approximation expansion
3.149	Resistances Weigh Series, Conductances Weigh Parallel	Difficulty 2 of 5	Uniqueness 2 of 5	approximation expansion · kirchhoff rules
3.150	Symmetry Folds the Resistor Cube	Difficulty 3 of 5	Uniqueness 3 of 5	symmetry · kirchhoff rules
3.151	A Termination That Hides the Length	Difficulty 3 of 5	Uniqueness 4 of 5	kirchhoff rules · symmetry
3.152	The Chain That Contains Itself	Difficulty 2 of 5	Uniqueness 3 of 5	kirchhoff rules · symmetry
3.153	Half the Current Takes the Shortcut	Difficulty 4 of 5	Uniqueness 5 of 5	superposition · symmetry · kirchhoff rules
3.154	Current Spreading Out of an Axis	Difficulty 2 of 5	Uniqueness 2 of 5	resistance integration · local ohm law · current density · symmetry
3.155	The Resistance Lives Near the Ball	Difficulty 2 of 5	Uniqueness 3 of 5	resistance integration · local ohm law · current density · limiting cases
3.156	A Leaky Capacitor Times Itself	Difficulty 3 of 5	Uniqueness 3 of 5	resistance integration · rc transient · capacitance · local ohm law
3.157	Two Spreading Resistances in Series	Difficulty 2 of 5	Uniqueness 3 of 5	local ohm law · superposition · resistance integration · approximation expansion
3.158	A Ball, a Plane and Its Mirror	Difficulty 3 of 5	Uniqueness 3 of 5	method of images · local ohm law · current density · approximation expansion
3.159	Leakage Between Two Parallel Wires	Difficulty 3 of 5	Uniqueness 2 of 5	local ohm law · superposition · current density · symmetry
3.160	Leakage Read Off the Capacitance	Difficulty 1 of 5	Uniqueness 3 of 5	capacitance · local ohm law · resistance integration
3.161	One Flux Gives Charge and Current	Difficulty 2 of 5	Uniqueness 4 of 5	gauss law · local ohm law · capacitance
3.162	Where Current Cannot Cross	Difficulty 3 of 5	Uniqueness 4 of 5	dielectric boundary · local ohm law · gauss law
3.163	Thin Layers of a Graded Conductor	Difficulty 2 of 5	Uniqueness 2 of 5	resistance integration · local ohm law · current density · limiting cases
3.164	Current Lines Bend Like Field Lines	Difficulty 2 of 5	Uniqueness 3 of 5	local ohm law · current density · dielectric boundary
3.165	Charge Where the Resistivity Jumps	Difficulty 2 of 5	Uniqueness 4 of 5	local ohm law · gauss law · current density
3.166	Equal Relaxation Times Leave No Charge	Difficulty 3 of 5	Uniqueness 4 of 5	local ohm law · current density · gauss law · dielectric boundary
3.167	Only the End Values Count	Difficulty 3 of 5	Uniqueness 3 of 5	local ohm law · current density · gauss law
3.168	A Linear Resistivity Gives Uniform Charge	Difficulty 2 of 5	Uniqueness 3 of 5	local ohm law · current density · gauss law
3.169	Current Crowds Toward the Surface	Difficulty 2 of 5	Uniqueness 3 of 5	resistance integration · local ohm law · current density
3.170	Ninety Percent Needs 2.3 Time Constants	Difficulty 1 of 5	Uniqueness 1 of 5	rc transient · differential equation
3.171	The Filler Sets the Leak Time	Difficulty 2 of 5	Uniqueness 3 of 5	rc transient · gauss law · local ohm law
3.172	Cutting the Capacitance Drives Current Back	Difficulty 3 of 5	Uniqueness 3 of 5	rc transient · kirchhoff rules · differential equation
3.173	Two Readings Fix the Voltmeter	Difficulty 2 of 5	Uniqueness 3 of 5	kirchhoff rules · limiting cases
3.174	Walking the Loop Between Two Points	Difficulty 1 of 5	Uniqueness 2 of 5	kirchhoff rules · electric potential
3.175	The Weaker Source Goes Silent	Difficulty 2 of 5	Uniqueness 2 of 5	kirchhoff rules · limiting cases
3.176	A Current with No Voltage	Difficulty 2 of 5	Uniqueness 5 of 5	kirchhoff rules · electric potential · symmetry
3.177	The Capacitor Reads One Resistor	Difficulty 2 of 5	Uniqueness 3 of 5	kirchhoff rules · electric potential · capacitance
3.178	Two Loads on a Real Source	Difficulty 1 of 5	Uniqueness 1 of 5	kirchhoff rules · limiting cases
3.179	The Loaded Potentiometer Sags	Difficulty 2 of 5	Uniqueness 3 of 5	kirchhoff rules · approximation expansion · limiting cases
3.180	Two Batteries Become One	Difficulty 2 of 5	Uniqueness 3 of 5	kirchhoff rules · limiting cases
3.181	Three Branches, One Node Equation	Difficulty 2 of 5	Uniqueness 2 of 5	kirchhoff rules · electric potential
3.182	Three Sources Between Two Nodes	Difficulty 2 of 5	Uniqueness 2 of 5	kirchhoff rules · electric potential
3.183	The Ideal Source Hides a Resistor	Difficulty 3 of 5	Uniqueness 3 of 5	kirchhoff rules · superposition · electric potential
3.184	A Capacitor Reads Two Cells	Difficulty 3 of 5	Uniqueness 2 of 5	kirchhoff rules · capacitor networks · electric potential
3.185	The Star Point Weighs Its Neighbours	Difficulty 2 of 5	Uniqueness 2 of 5	kirchhoff rules · electric potential
3.186	A Bare Wire Across the Bridge	Difficulty 2 of 5	Uniqueness 3 of 5	kirchhoff rules · limiting cases
3.187	Turning the Crossed Bridge Around	Difficulty 3 of 5	Uniqueness 4 of 5	kirchhoff rules · symmetry · limiting cases
3.188	Half the Emf, Twice as Fast	Difficulty 3 of 5	Uniqueness 3 of 5	rc transient · kirchhoff rules · differential equation
3.189	Same Charge, Different Heat	Difficulty 2 of 5	Uniqueness 3 of 5	joule heating · rc transient
3.190	Two Wires Make Three Parallel	Difficulty 2 of 5	Uniqueness 3 of 5	max power transfer · optimization · kirchhoff rules
3.191	Currents Split to Waste Least	Difficulty 1 of 5	Uniqueness 3 of 5	joule heating · optimization · kirchhoff rules
3.192	Where a Battery's Power Goes	Difficulty 2 of 5	Uniqueness 3 of 5	joule heating · energy conservation · kirchhoff rules
3.193	Half the Input Turns the Shaft	Difficulty 2 of 5	Uniqueness 3 of 5	joule heating · optimization · max power transfer
3.194	Thinner Filament Needs More Voltage	Difficulty 2 of 5	Uniqueness 3 of 5	joule heating · resistance integration · approximation expansion
3.195	Heating Toward a Joule Balance	Difficulty 2 of 5	Uniqueness 2 of 5	joule heating · differential equation · energy conservation
3.196	Where the Power Curve Is Flat	Difficulty 2 of 5	Uniqueness 3 of 5	kirchhoff rules · joule heating · max power transfer · optimization
3.197	Two Sources Feeding One Load	Difficulty 3 of 5	Uniqueness 3 of 5	kirchhoff rules · max power transfer · optimization · joule heating
3.198	Grouping Cells to Match the Load	Difficulty 2 of 5	Uniqueness 3 of 5	max power transfer · optimization · kirchhoff rules
3.199	Two Resistors Share the Stored Energy	Difficulty 2 of 5	Uniqueness 3 of 5	field energy · joule heating · energy conservation · rc transient
3.200	The Source Takes Back Twice	Difficulty 3 of 5	Uniqueness 3 of 5	capacitance · field energy · work energy · energy conservation
3.201	Pulling Glass Against a Fixed Voltage	Difficulty 2 of 5	Uniqueness 2 of 5	capacitance · field energy · work energy · dielectric polarization
3.202	A Voltage Lifts the Water	Difficulty 2 of 5	Uniqueness 3 of 5	capacitance · field energy · electrostatic force · hydrostatics
3.203	A Leak Set by the Medium Alone	Difficulty 2 of 5	Uniqueness 4 of 5	local ohm law · gauss law · rc transient · joule heating
3.204	A Fifth of the Charge	Difficulty 1 of 5	Uniqueness 2 of 5	rc transient · joule heating · differential equation
3.205	Half the Energy Is Always Lost	Difficulty 2 of 5	Uniqueness 3 of 5	rc transient · kirchhoff rules · joule heating · energy conservation
3.206	Weighing the Carriers by Braking	Difficulty 3 of 5	Uniqueness 5 of 5	non inertial frame · conduction mechanisms · local ohm law
3.207	The Momentum Hidden in a Current	Difficulty 1 of 5	Uniqueness 3 of 5	current density · conduction mechanisms
3.208	A Long Walk for a Short Drift	Difficulty 2 of 5	Uniqueness 3 of 5	current density · conduction mechanisms · approximation expansion
3.209	A Month in Transit, a Meganewton Push	Difficulty 2 of 5	Uniqueness 3 of 5	current density · local ohm law · conduction mechanisms
3.210	The Field Inside a Proton Beam	Difficulty 2 of 5	Uniqueness 3 of 5	gauss law · electric potential · current density · energy conservation
3.211	The Four Thirds Law of a Diode	Difficulty 2 of 5	Uniqueness 4 of 5	poisson equation · energy conservation · current density
3.212	Counting Ions Through Their Drift	Difficulty 2 of 5	Uniqueness 2 of 5	conduction mechanisms · current density · local ohm law
3.213	Ions That Must Cross in Half a Period	Difficulty 3 of 5	Uniqueness 4 of 5	conduction mechanisms · calculus of motion · optimization
3.214	Saturation Counts, Recombination Balances	Difficulty 2 of 5	Uniqueness 2 of 5	conduction mechanisms · differential equation
3.215	Ions Fading by Pairs	Difficulty 2 of 5	Uniqueness 3 of 5	conduction mechanisms · differential equation
3.216	Cosmic Rays Drain a Capacitor	Difficulty 2 of 5	Uniqueness 3 of 5	conduction mechanisms · capacitance
3.217	An Avalanche Grows Exponentially	Difficulty 2 of 5	Uniqueness 3 of 5	conduction mechanisms · differential equation
3.218	Avalanches Started Everywhere at Once	Difficulty 3 of 5	Uniqueness 3 of 5	conduction mechanisms · differential equation · superposition