Analyze electrical circuits and components

Explain voltage as potential energy per unit charge, and reason about how a charge gains and loses energy in a circuit.

Explain current as the flow of charge, and predict its direction by reasoning about potential differences.

Explain resistance as a control on the rate of energy conversion, and apply Ohm's law as an expression of this relationship.

Explain power in a circuit element and distinguish between energy delivery and energy dissipation.

Describe how ideal voltmeters and ammeters measure circuit quantities, and relate their properties (infinite/zero resistance) to their function.

Sketch and interpret the I-V characteristic of a resistor and explain what its slope represents physically.

Explain what ideal voltage and current sources enforce in a circuit, and sketch their I-V characteristics.

Reason about the physical result of combining voltage sources in series versus parallel, including why certain configurations are invalid.

Reason about the physical result of combining current sources in parallel versus series, including why certain configurations are invalid.

Explain Kirchhoff's Current Law (KCL) as conservation of charge and use it to reason about how current distributes at a node.

Explain Kirchhoff's Voltage Law (KVL) as conservation of energy and use it to reason about how voltage distributes around a loop.

Qualitatively predict how current and voltage redistribute when a component is added to or removed from a simple circuit.

Solve a simple resistive circuit by combining physical reasoning with KCL, KVL, and Ohm's law.

Explain physically why series combination increases total resistance and derive the equivalent resistance formula.

Explain physically why parallel combination decreases total resistance and derive the equivalent resistance formula.

Apply the voltage divider rule to series circuits and explain intuitively why voltage splits proportionally to resistance.

Apply the current divider rule to parallel circuits and explain intuitively why current splits inversely with resistance.

Identify all nodes in a circuit, assign node voltages relative to a reference, and explain why they are sufficient to describe the circuit.

Formulate KCL equations at each non-reference node in terms of unknown node voltages.

Solve the system of linear equations from nodal analysis to find all node voltages and branch currents.

Handle voltage sources in nodal analysis using the supernode technique and explain the reasoning behind it.

Identify all meshes in a planar circuit, assign mesh currents, and explain why they are sufficient to describe the circuit.

Formulate KVL equations for each mesh by expressing voltage changes in terms of mesh currents.

Handle current sources in mesh analysis using the supermesh technique and explain the reasoning behind it.

Solve the system of mesh equations to find all mesh currents and branch voltages.

Compare nodal and mesh analysis for a given circuit and choose the more efficient method based on its structure.

Determine the equivalent resistance of a resistive ladder network by identifying its repeating pattern and setting up a recursive relationship.

Determine the equivalent resistance of a resistive cube network by applying symmetry arguments to simplify the analysis.

Verify the solution of a complex network problem by checking for physical consistency, such as power balance.

Explain how a capacitor stores energy in an electric field and use Q=CV to relate its charge, voltage, and capacitance.

Explain how an inductor stores energy in a magnetic field and use V=L(di/dt) to relate its voltage to the rate of change of current.

Calculate the energy stored in a capacitor and an inductor.

Derive the equivalent capacitance and inductance for series and parallel combinations and explain why the rules differ from resistors.

Describe a sinusoidal signal using amplitude, frequency, period, and phase, and explain what each parameter represents physically.

Explain the difference between instantaneous and average power for time-varying signals.

Conceptually explain how complex periodic waveforms can be viewed as a sum of simple sinusoidal harmonics.

Explain the operating principle of a DC motor based on the conversion of electrical energy to mechanical energy via electromagnetic forces.

Explain the operating principle of a DC generator based on the conversion of mechanical energy to electrical energy via electromagnetic induction.

Calculate electricity consumption and cost for household appliances and reason about what drives high energy usage.