PHYS 2213 Prelim 2

What is a capacitor physically?

Stores charge and energy in an electric field

What is the defining equation of a capacitor?

Q = CV

What does C represent?

Capacitance = ability to store charge per voltage

What does R represent?

Resistance = how much a component resists current

What is current I?

Rate of charge flow which is I = dQ/dt

What does epsilon represent?

Battery voltage (emf), the “push” driving current

What is the voltage across a capacitor in terms of charge?

V = Q/C

Can capacitor voltage change instantly?

No, the voltage is continuous

What happens to a capacitor at long time?

Acts like an open circuit (no current)

At long time, what is the current through a capacitor?

I = 0

At long time, what is the current through a capacitor?

I = 0

At long time, what determines capacitor voltage

The circuit reduces to DC → capacitor takes steady-state voltage

What is the time constant

T = RC

Charging equation for charge?

Q(t) = Q_f(1 - e^-t/T)

Discharging equation?

Q(t) = Q₀e^-t/T

What is Q_f?

Final (maximum) charge = C epsilon

What is Kirchhoff’s Voltage Law?

Sum of voltage changes around a loop = 0

What is the voltage across a resistor?

V = IR

What is the voltage across a capacitor?

V = Q/C

In a charging loop, what is the equation form?

epsilon = IR + Q/C

What does a switch do?

Changes which parts of the circuit are connected

When switch changes, what stays the same instantly?

Capacitor voltage

When switch changes, what can change instantly?

Current

How do you analyze after a switch?

Redraw the circuit after the switch

When are resistors in series?

One path, no branching

When are resistors in parallel?

Same two nodes

What is the quick test?

Can current split? Yes if parallel, no if series

“Very long time” means what?

Capacitor = open circuit, I = 0

“Immediately after switching” means what?

Capacitor voltage unchanged

“Find dQ/dt” means what

Find current

If capacitor is fully charged, what is voltage across it?

Equals battery voltage (in simple circuits)

Why does the current decrease during charging?

Capacitor builds voltage that opposes battery?

What is the effective driving voltage?

epsilon - Q/C

What happens if V_c= epsilon?

Current becomes 0

What do you do first in RC problems?

Identify what the circuit looks like after switching

What do you do second in RC problems?

Find equivalent resistance seen by capacitor

What do you do third?

Use:
- KVL OR

• standard RC formulas