Capacitors

DC Circuits Containing Resistors and Capacitors

By Rachel Wampler

Capacitors

• ​Shown is a circuit with a capacitor, resistor, and battery

• Initially capacitor is uncharged

• when battery connected current flows to charge capacitor

• As the charge builds up, there is increased resistance because of the repulsion of the charges on the parallel plates

• When capacitor is fully charged, no current will flow.

  • ​Current no longer flows because the parallel plates aren't connected and can't accept anymore charge.

Formulas: Loop Rule

Formulas: Charging a Capcitor

Formulas: Discharging a Capacitor

Capacitor Applications

• Camera flashes work by charging a capacitor with a battery

  • Usually has a large time constant because batteries cannot produce charge very fast

• The capacitor is then discharged through the flashbulb circuit with a short time constant​

Multiple Choice

An uncharged capacitor and resistor care connected in series to a battery.

If V = 12 V , C = 5 μF, and R = 8x10⁵ Ω. Find the time constant, max charge, max current, and charge as a function of time.

• 𝜏 = 8 s

  Q = 60 μC

  I = 30 μA

  q(t) = 60 (1-e^-t/4) μC

• 𝜏 = 4 s

  Q = 120 μC

  I = 15 μA

  I(t) = 15e^-t/4μ

• 𝜏 = 8 s

  Q = 120 μC

  I = 30 μA

  I(t) = 15e^-t/4μ

• 𝜏 = 4 s

  Q = 60 μC

  I = 15 μA

  q(t) = 60 (1-e^-t/4) μC