Electric Field and Potential Relationship

Study Notes

Relationship Between Electric Field and Potential

• Electric potential (V) is the amount of potential energy per unit charge at a point in an electric field, measured in volts (V). • Electric field strength (E) is a vector quantity defined as the force per unit charge on a test charge, measured in Newton/Coulomb (N/C) or V/m.

Electric Field and Potential Relationship

• Electric potential difference is the difference in electric potential between two points in an electric circuit, measured in volts (V). • Electric field and electric potential are related through the equation: E = -dV/dr

Potential Energy in an Electric Field

• The potential energy (U) of a charge (q) in an electric field is given by: U = qV • Potential energy is the energy associated with the arrangement of charges in an electric field.

Capacitors

• Capacitors are passive electronic components consisting of two or more pieces of conducting material separated by an insulating material. • Capacitors store energy in the form of an electrical charge, producing a potential difference (static voltage) across its plates. • Types of capacitors: Ceramic, Electrolytic, Tantalum, Film, Variable, Supercapacitors (Ultracapacitors), Mica

Capacitor Construction and Operation

• A capacitor consists of two or more parallel conductive plates separated by an insulating material (dielectric). • The dielectric of a capacitor is non-conductive and blocks DC current flow. • When a capacitor is connected to an AC circuit, the current appears to pass through the capacitor with little or no resistance. • A capacitor charges up to its supply voltage, and a potential difference is established between the two plates.

Capacitor Properties

• Capacitance (C) is the property of a capacitor to store charge on its plates in the form of an electrostatic field, measured in Farads (F). • Capacitance is proportional to the area of the plates and inversely proportional to the distance between them. • The generalized equation for the capacitance of a parallel plate capacitor is: C = ε(A/d) • The dielectric constant (ε) is the permittivity of the dielectric material being used.

Worked Examples

• Example 1: A capacitor stores a charge of 10 μC when a voltage of 50 V is applied across it. Determine the capacitance of the capacitor. • Example 2: Calculate the energy stored in a capacitor with a capacitance of 100 μF when it is charged to a potential difference of 12 V. • Example 3: A capacitor is connected to a 12 V battery and stores a charge of 8 mC. Calculate the capacitance of the capacitor. • Example 4: A capacitor is initially uncharged. If a charge of 20 μC is transferred to it, and the potential difference across the capacitor becomes 40 V, calculate its capacitance.