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Ohm's law states that the electric current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, [1] one arrives at the three mathematical equations used to describe this relationship: [2]
Mechanical impedance is the ratio of a potential (e.g., force) to a flow (e.g., velocity) where the arguments of the real (or imaginary) parts of both increase linearly with time. Examples of potentials are: force, sound pressure, voltage, temperature. Examples of flows are: velocity, volume velocity, current, heat flow.
The input impedance of an infinite line is equal to the characteristic impedance since the transmitted wave is never reflected back from the end. Equivalently: The characteristic impedance of a line is that impedance which, when terminating an arbitrary length of line at its output, produces an input impedance of equal value. This is so because ...
This is analogous to electrical impedance, that is the ratio of voltage output to current input (e.g. resistance is voltage divided by current). A "spring constant" defines the force output for a displacement (extension or compression) of the spring. A "damping constant" defines the force output for a velocity input. If we control the impedance ...
Snap, [6] or jounce, [2] is the fourth derivative of the position vector with respect to time, or the rate of change of the jerk with respect to time. [4] Equivalently, it is the second derivative of acceleration or the third derivative of velocity, and is defined by any of the following equivalent expressions: = ȷ = = =.
Without the presence of an electric field, the electrons have no net velocity. When a DC voltage is applied, the electron drift velocity will increase in speed proportionally to the strength of the electric field. The drift velocity in a 2 mm diameter copper wire in 1 ampere current is approximately 8 cm per hour. AC voltages cause no net movement.
Henri Poincaré in 1907 was the first to describe a transducer as a pair of linear algebraic equations relating electrical variables (voltage and current) to mechanical variables (force and velocity). [29] Wegel, in 1921, was the first to express these equations in terms of mechanical impedance as well as electrical impedance. [30]
If a mechanical system has no losses, then the input power must equal the output power. This provides a simple formula for the mechanical advantage of the system. Let the input power to a device be a force F A acting on a point that moves with velocity v A and the output power be a force F B acts on a point that moves with velocity v B.