electric 2.2 - RC circuits.pp

R-C Series Circuit

A circuit composed of a resistor (R) and a capacitor (C) connected in series.

Time Constant (τ)

The time required for the voltage across the capacitor to decrease to approximately 37% of its initial value.

Exponential Curve

A curve that describes the natural response of voltage and current in an R-C circuit.

Energy Stored in Capacitor (Wc)

Calculated as Wc = 1/2 C V^2, representing energy stored in a capacitor.

Natural Response

The behavior of a circuit without external forcing functions, determined by the circuit's own characteristics.

Forcing Function

An external signal or voltage source that drives the circuit's behavior.

DC Voltage (V0)

A constant voltage supply that does not change with time, used in R-C circuits.

Initial Condition

The state of a circuit at the start of an observation, often at time t = 0.

Discharge of Capacitor

The process of releasing energy stored in a capacitor.

• When a capacitor is connected to a circuit, it discharges its energy.

• This flow of energy leads to a reduction in voltage across the capacitor.

• The decrease in voltage follows an exponential pattern, determined by the 'time constant' of the circuit, which defines how quickly the voltage drops.

Differential Equation

An equation involving derivatives that describes the relationship between a function and its rates of change.

Homogeneous System

A system of equations where all terms are equal to zero, with no external input.

Stored Energy

The energy retained in a capacitor, calculated based on its voltage and capacitance.

What happens to VC when the switch is opened after the capacitor has been fully charged?

When the switch is opened after the capacitor has reached full charge, the voltage across the capacitor (VC) remains unchanged because there is no route for the stored energy to discharge, provided there is no resistor connected. The voltage stays steady until a load is introduced or due to leakage.