Simple RC circuits Chapter 12. AC circuits

When discussing the AC circuit in two ways:

1) V and I change with respect to time; (time domain analysis)

2) changes in amplitude with the signal frequency. (Frequency domain analysis)

A simple RC circuit analysis

The capacitive formula available I=C\frac{\mathrm{dV} }{\mathrm{d} t}=-\frac{V}{R}

Solution of differential equations above:V=Ae^{^{-\frac{t}{RC}}}

Derived as follows:

C fully charged after the discharge of the resistor R in parallel, the discharge curve:

 5RC rule of thumb is: when the time t >> 5RC, V charge / discharge to about 1% of the final value.

The time constant of the RC product is called the circuit;

Second, a simple RC circuit battery +

 The circuit I=C\frac{\mathrm{dV} }{\mathrm{d} t}=\frac{Vi-V}{R}equation: ;

Solution:V = Vi + Ae '{^ {- \ frac {t} {RC}}} ;

A is a constant determined by the initial conditions, when t = 0 V = 0, so that A = -Vi;

So  V = I + Ae ^ {^ {- \ frac {t} {RC}}} = There \ left (1-e ^ {^ {- t / RC}} \ right);

The derivation process

Charging curve:

Rising from 10% to 90% of the time is 2.2RC. 

Derivation:

 

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Origin blog.csdn.net/weixin_42143745/article/details/90523588