An approximate expression for the motional capacitance of a lateral field resonator

The parallel RLC circuit is an arrangement where the resistor (R), inductor (L), and capacitor (C) are all connected to the same nodes and, as a result, share the same voltage across them. The parallel RLC circuit is analyzed in terms of admittance (Y), which reflects the ease with which current can flow. The admittance is given 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...

Consider designing an oscillator circuit, a crucial component in various electronic devices and systems. The objective is to create an oscillator circuit with specific characteristics: a damped natural frequency of 4 kHz and a damping factor of 4 radians per second. To accomplish this, a parallel RLC circuit is employed, known for its ability to sustain oscillations at a resonant frequency. In this case, the damping factor is pivotal in achieving the desired performance.
Starting with a fixed...

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...

The property of an inductor makes it resist any change in the current passing through it, while the property of a capacitor is to build up the charge across its terminals. Hence, if an inductor and capacitor are connected in series, they have opposite effects on the relative phase between current and voltage. The current through the circuit undergoes forced oscillation at the frequency of the source. The resistance term in an R-L-C circuit acts as a damping term because power is dissipated...