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The RC time constant, denoted τ (lowercase tau), the time constant (in seconds) of a resistor–capacitor circuit (RC circuit), is equal to the product of the circuit resistance (in ohms) and the circuit capacitance (in farads):
These equations show that a series RC circuit has a time constant, usually denoted τ = RC being the time it takes the voltage across the component to either rise (across the capacitor) or fall (across the resistor) to within 1 / e of its final value. That is, τ is the time it takes V C to reach V(1 − 1 / e ) and V R to reach ...
These equations show that a series RL circuit has a time constant, usually denoted τ = L / R being the time it takes the voltage across the component to either fall (across the inductor) or rise (across the resistor) to within 1 / e of its final value. That is, τ is the time it takes V L to reach V( 1 / e ) and V R to ...
First order LTI systems are characterized by the differential equation + = where τ represents the exponential decay constant and V is a function of time t = (). The right-hand side is the forcing function f(t) describing an external driving function of time, which can be regarded as the system input, to which V(t) is the response, or system output.
A parallel resonant circuit provides current magnification. A parallel resonant circuit can be used as load impedance in output circuits of RF amplifiers. Due to high impedance, the gain of amplifier is maximum at resonant frequency. Both parallel and series resonant circuits are used in induction heating.
which is a second-order partial differential equation (PDE). By a simple rearrangement of equation (see later) it is possible to make two important terms appear, namely the length constant (sometimes referred to as the space constant) denoted and the time constant denoted . The following sections focus on these terms.
An increase in this variable means the higher pole is further above the corner frequency. The y-axis is the ratio of the OCTC (open-circuit time constant) estimate to the true time constant. For the lowest pole use curve T_1; this curve refers to the corner frequency; and for the higher pole use curve T_2. The worst agreement is for τ 1 = τ 2.
Denote the serial time as and the parallel time as , where + =. Denote the number of processors as N {\displaystyle N} . Hypothetically, when running the program on a serial system (only one processor), the serial part still takes s {\displaystyle s} , while the parallel part now takes N p {\displaystyle Np} .