Simple formulas for the trapping rate by nonspherical absorber and capacitance of nonspherical conductor

A spherical capacitor consists of two concentric conducting spherical shells of radii R1 (inner shell) and R2 (outer shell). The shells have equal and opposite charges of +Q and −Q, respectively. For an isolated conducting spherical capacitor, the radius of the outer shell can be considered to be infinite.
Conventionally, considering the symmetry, the electric field between the concentric shells of a spherical capacitor is directed radially outward. The magnitude of the field, calculated by...

From the study of resistive circuits, it is understood that employing a series-parallel combination serves as an effective strategy for simplifying circuits. Capacitors can be arranged within a circuit in one of two ways: a series configuration or a parallel configuration. The way these capacitors are connected to a battery will influence both the potential drop across each individual capacitor and the size of the charge that each capacitor can store. This is determined by the specific type of...

Multiple capacitors can be connected in a circuit in series or parallel configuration. When the capacitor combination is connected to a battery, the potential drop across each capacitor and the magnitude of charge stored in the individual capacitor depends on the type of the connection. The capacitor combination is replaced by a single equivalent capacitor that stores the same amount of charge as the combination for a given potential difference.
The following strategies are adopted to calculate...

In electrical power systems, understanding the capacitance of transmission lines is fundamental for efficient operation.
Single-Phase Lines
Consider a single-phase, two-wire transmission line with equal phase spacing energized by a voltage source. One conductor carries a uniform positive charge, while the other carries an equal negative charge. The capacitance C of the line can be derived from the voltage V between the conductors. For a one-meter section of the line, the capacitance is given...

Capacitors play a crucial role in car radios, where they filter and store frequencies to ensure clear signal reception. Essentially serving as energy storage devices, capacitors store energy within their electric field and are composed of two parallel conducting plates separated by a dielectric.
When a voltage source is connected to a capacitor, positive and negative charges accumulate on the opposite plates. This accumulation generates a potential difference that equals the product of the...

In the domain of radio communication, the significance of impedance matching must be considered. It is crucial to ensure the efficient transmission of signals between radio transmitters and receivers. Achieving this balance involves using impedance-matching circuits, with one fundamental configuration comprising a resistor, capacitor, and inductor.
The process of harmonizing these impedances begins with a clear understanding of the input and output signals. Once these signals are known, the...