(358) 08.4: Potential and Field-Introduction to Capacitors

Electric Fields and Electric Potentials

  • Transitioning to studying capacitors as the first electric circuit device.

Kirchhoff's Loop Law

  • Important principle related to capacitors in electric circuits.

  • States that in any closed loop in a circuit, the sum of the voltage changes equals zero.

  • Example process:

    • Starting from a voltage of 20 V, moving to 40 V results in +20 V change.

    • Moving along an equipotential surface results in 0 V change.

    • Returning from 40 V to 30 V yields -10 V change.

    • The sum is: +20 V + 0 V - 10 V + 0 V - 10 V + 0 V = 0 V.

  • Implication: Electric force is conservative; energy change in a loop is zero.

Introduction to Capacitors

  • Definition: Device used to store electric charge.

  • Basic structure: Composed of two plates separated by a small distance.

  • Plates hold equal and opposite charges (+q on one plate, -q on the other).

Capacitor Geometry

  • Common configuration: Parallel plate capacitor, often designed as cylindrical for compactness.

  • Construction: Thin strips of aluminized mylar rolled with insulating material, forming cylindrical shape.

Electric Field in Capacitors

  • Inside the capacitor, the electric field is approximately uniform.

  • A voltage difference exists across the plates, corresponding to an electric field running from high to low potential.

Capacitance

  • Defined as the charge a capacitor can hold per unit voltage applied: ( C = \frac{Q}{V} )

  • Units: Coulombs per Volt = Farad (F), named after Michael Faraday.

  • Value range: Typical capacitors found on circuit boards are measured in picofarads (pF) to microfarads (µF).

    • 1 pF = 10^{-12} F; manufacturers often use these prefixes distinctively.

  • Specialized applications can have capacitors rated up to 1 F or more.

Practical Applications of Capacitors

  • Used to store charge for devices requiring quick bursts of energy (e.g., camera flashes).

  • Regulate power supply fluctuations, protecting devices from sudden outages (e.g. computers).

  • Larger capacitors found in high-voltage applications, like audio systems.

Charging a Capacitor

  • Circuit setup: battery, capacitor, switch, and wires.

  • Upon closing the switch, a circuit is completed, allowing electric charges to flow.

  • Battery acts as a conveyor belt, moving charges from one plate to another.

Charge Accumulation

  • One plate (positive) gains electrons, becoming negatively charged.

  • The opposite plate loses electrons, resulting in a positive charge.

  • Charging continues until the voltage across the capacitor equals battery EMF (electromotive force).

  • A charged capacitor behaves like an open circuit, halting further current flow.

Electric Field Dynamics

  • Electric field inside the capacitor is perpendicular to equipotential surfaces.

  • Slight electric field exists outside the capacitor; it influences overall charge movement.

  • Once the capacitor is fully charged, equilibrium is reached, preventing further charge movement.

Conclusion

  • Future discussions will include determining capacitance for various capacitor shapes and their behavior in circuits.