Deriving equations for voltage and current as functions of time in an RC circuit where the capacitor is being charged.

Deriving equations for voltage and current as functions of time in an RC circuit where the capacitor is being discharged.

Graphs of the voltage and current in an RC circuit with a square wave power supply.

Ideal battery is defined. Batteries and capacitors in series and in parallel, with diagrams.

Charging and discharging a capacitor, with diagrams and derived equations for charge on the capacitor and current through the circuit as functions of time. Exponential decay and time constant tau.

Conceptual overview of the RC circuit, with definition of exponential decay and the time constant.

Charging and discharging capacitors; differential equation and solution; time constant; examples.

Relation between voltage and charge (Q = VC); equivalent capacitance for parallel and series capacitors.

Detailed strategy for using Kirchhoff's rules; equivalent resistance; impedance matching; RC circuit; resistor networks.

Differential equation and solution for q(t) for charging and discharging capacitors; current and time constant.

Three questions with answers and explanations.

Finding charge as a function of time, as well as maximum power delivered.

Solution (PDF)^#

Stored energy and potential difference after inserting a dielectric.

Solution (PDF)^#

6-part problem; potentials of capacitor plates and voltages in circuit before and after connection; doubled capacitor distance.

Solution (PDF)^#

Calculating rate of change of E-field, and B-field of charging capacitor.

Solution (PDF)^#

4-part problem; finding charge and electric field for each capacitor in circuit.

Solution (PDF)

5-part problem; differential equation and solution; current, energy, and heat at time t₁>0.

Solution (PDF)