In the book Practical electronics for inventors there is a part about capacitors that got me puzzled. It states the following about RC circuit behaviour:
"By applying Kirchhoff's coltage law to the circuit, you can set up the following expression to figure out how the current will behave after the switch is closed:
V0=IR + 1/C *⌠Idt
To get rid of the integral, differentiate each term:
0=R* dI/dt + 1/C*I or dI/dt + 1/RC*I = 0
This expression is a linear, first-order, homogenous differential equation that has the following solution:
I=I0e^-t/RC"
I cant understand how it arrived to this conclusion, can someone help me?
Thanks.
Edit: I mean how it solved the differential equation that is.
"By applying Kirchhoff's coltage law to the circuit, you can set up the following expression to figure out how the current will behave after the switch is closed:
V0=IR + 1/C *⌠Idt
To get rid of the integral, differentiate each term:
0=R* dI/dt + 1/C*I or dI/dt + 1/RC*I = 0
This expression is a linear, first-order, homogenous differential equation that has the following solution:
I=I0e^-t/RC"
I cant understand how it arrived to this conclusion, can someone help me?
Thanks.
Edit: I mean how it solved the differential equation that is.