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3. Provides a common formula for constant current charge and discharge:? Vc? T/C. Here's another common formula for capacitive charging: 1-e-t / r / c). In the RC circuit charging formula Vcn (1-e-t / R) is the negative exponential term of e. About the capacitance used for delay how to use the capacitance is better, can not generalize, the specific situation specific analysis. The actual capacitance has parallel insulation resistance, series lead inductor and lead resistance. There are more complex modes-resulting in adsorption effects and so on. For reference.
E is the amplitude of a voltage source. By closing a switch, a step signal is formed and the capacitance C is charged by resistance R. E may also be a high level amplitude of a continuous pulse signal whose amplitude varies from a low 0 V level to a high level amplitude. The variation rule of voltage V _ c at both ends of capacitance with time is the charge formula Vc _ (E _ (1) -e ~ (-) t / r ~ (1) C _ (n). One of them is the negative exponent of e, and it doesn't show up here, and it needs special attention. T in the expression is a time variable, and a small e is a natural exponential term. For example, if t = 0, the 0 power of e is 1, we calculate that VC is equal to 0 V. It accords with the law that the voltage at both ends of the capacitor can not change. For constant current charge and discharge formula:? Vc? T / C, which comes from the formula: VcQ / C / C. For example, a constant current source with a current amplitude of 1A (that is, its output amplitude does not vary with the output voltage) charges or discharges the capacitor. It can be seen from the formula that the capacitance voltage increases or decreases linearly with time. This is how many triangular or sawtooth waves are produced. According to the numerical value and formula, it can be calculated that the change rate of capacitance voltage is 1V/mS. This means that you can get a 5 V capacitance voltage change using the 5mS time; in other words, a 2 V change in VC is known, and it can be calculated that it has gone through the 2mS time course. Of course, C and I in this relation can also be variables or references. Please refer to the relevant teaching materials for details. For reference.
4. First, let the charge of the capacitor plate at t time be Q, and the voltage between the electrodes be u.
And because u=q/C, I=dq/dt (where d stands for differential), after it is substituted: U-q/C=R*dq/dt,
This is called Rdq / U / Q / C / DT, and then the indefinite integral is obtained on both sides, and the q=CU is obtained by using the initial condition of: t0 / Q0 [1-e ^ -t / r / r] this is the function of the change of charge on the capacitor plate with time t. By the way, RC is often referred to as a time constant in electrotechnics. Correspondingly, using u = q/C, the function of the plate voltage over time is immediately obtained, u = U[1-e^-t/(RC)]. From the formula obtained, it is only when time t tends to infinity that the charge and voltage on the plate are stable and the charging is considered to be over.
But in the practical problem, because 1-e ^ -t / r / c) is fast approaching 1, after a very short period of time, the change of the charge and voltage between the electrodes of the capacitor has been very little. Even if we use highly sensitive electrical instruments, we can not detect the small changes in Q and u, so it can be considered that the balance has been reached and the charging is over.
. It can be said that it is a moment of speed.