dVdq

dVdq refers to the change in voltage (dV) with respect to a change in charge (dq). It is a fundamental concept in electrical engineering and physics, particularly in the study of capacitors.

In the context of a capacitor, dVdq represents the reciprocal of capacitance, which is defined as the ratio of charge stored to the voltage across the capacitor. Mathematically, capacitance (C) is expressed as C = q/V, where q is the charge and V is the voltage. Therefore, dVdq is equal to 1/C.

This relationship highlights that for a given change in charge, a smaller dVdq implies a larger capacitance, meaning the capacitor can store more charge at a given voltage. Conversely, a larger dVdq indicates a smaller capacitance.

The concept of dVdq is also relevant in understanding the energy stored in a capacitor. The energy (U) stored in a capacitor is given by U = (1/2)CV^2. By substituting C = q/V, we get U = (1/2)qV. Differentiating this with respect to q, we find dU/dq = (1/2)V + (1/2)q(dV/dq). Using V = q/C and dV/dq = 1/C, we can simplify this to dU/dq = (1/2)(q/C) + (1/2)q(1/C) = q/C = V. This shows that the rate of change of energy with respect to charge is equal to the voltage.

In summary, dVdq is an important derivative that quantifies how voltage changes with respect to charge, and it is inversely proportional to capacitance, offering insight into a capacitor's ability to store electrical energy.