A capacitor consists of two isolated conductors (the plates) with charges +q and -q. Its capacitance C is defined from where V is the potential difference between the plates.

The proportionality constant C is called the capacitance of the capacitor. Its value depends only on the geometry of the plates and not on their charge or potential difference.

The capacitance depends on geometrical factors like the plate area (A) and the separation between the plates (d).

If there is a single isolated conducting sphere of radius R, then its capacitance is

Capacitors in Parallel

Capacitors in Series

The electric potential energy U of a charged capacitor

In vacuum, the energy density u (potential energy per unit volume) in a field of magnitude E is

If the space between the plates of a capacitor is completely filled with a dielectric material, the capacitance C in vacuum (or in air) is multiplied by the material’s dielectric constant κ, (Greek kappa) which is a number greater than 1. which means the capacitance increases by k

If the charge on the capacitor plates is maintained, as in this case by isolating the capacitor, the effect of a dielectric is to reduce the potential difference between the plates by:

To produce a steady flow of charge, you need a “charge pump,” a device that—by doing work on the charge carriers—maintains a potential difference between a pair of terminals.

then the emf (work per unit charge) of the device is

An ideal emf device is one that lacks any internal resistance. The potential difference between its terminals is equal to the emf.

A real emf device has internal resistance. The potential difference between its terminals is equal to the emf only if there is no current through the device.

three resistances connected in series to an ideal battery with emf. The potential difference is maintained across a and b by the battery.

Resistance in Parallel.

Junction rule (or Kirchhoff’s current law): The sum of the currents entering any junction in a circuit must equal the sum of the currents leaving that junction.

Loop rule (or Kirchhoff’s voltage law): The sum of the potential differences across all elements around any closed circuit loop must be zero.

Figure 27.1 Charges in motion through an area A. The time rate at which charge flows through the area is defined as the current I. The direction of the current is the direction in which positive charges flow when free to do so.

Average Electric Current Assume charges are moving perpendicular to a surface of area A If ΔQ is the amount of charge that passes through A in time Δt, then the average current is

As Fig. (a), any isolated conducting loop is all at the same potential. No electric field can exist within it or along its surface. As Fig. (b), If we insert a battery in the loop, the conducting loop is no longer at a single potential. Electric fields act inside the material, exerting forces on internal charges, causing them to move and thus establishing a current. The diagram assumes the motion of positive charges moving clockwise.

Figure shows a conductor with current i0 splitting at a junction into two branches.

The Directions of Currents: 1-The charges passing through the area could be positive or negative or both. 2-It is common to refer to any moving charge as a charge carrier. 3-It is conventional to assign to the current the same direction as the flow of positive charges. 4-The direction of current flow is opposite the direction of the flow of electrons.

Current i (a scalar quantity) is related to current density J (a vector quantity) by: where dA is a vector perpendicular to a surface element of area dA.

The current density J has the same direction as the velocity of the moving charges if they are positive charges and the opposite direction if the moving charges are negative.

J is the current density of a conductor. It is defined as the current per unit area. J = I / A = (nq)vd

ResThe resistance R of a conductor is defined as: -V is the potential difference across the conductor and i is the current through the conductor. -The SI unit of resistance is volt per ampere (V/A) or ohm (Ω)

we may deal with the resistivity ρ of the material:

the ohm-meter (m):

simply the reciprocal of its resistivity:

The resistance R of a conducting wire of length L and uniform cross section is:

Ohm’s law states electric current(I) is directly proportional to voltage(V) and inversely proportional to resistance(R).

Most metals obey Ohm’s law Materials that obey Ohm’s law are said to be Ohmic.

The power P, or rate of energy transfer, in an electrical device across which a potential difference V is maintained is:

Change in Electric Potential: If the particle moves through a potential difference ΔV, the change in the electric potential energy is

Work by the Field: The work W done by the electric force as the particle moves from i to f:24-1 Electric Potential Energy

Conservation of Energy: If a particle moves through a change ΔV in electric potential without an applied force acting on it, applying the conservation of mechanical energy gives the change in kinetic energy as

Work by an Applied Force: If some force in addition to the electric force acts on the particle, we account for that work

The name equipotential surface is given to any surface consisting of a continuous distribution of points having the same electric potential.