discription of electronic parts: DC circuits

Saturday, April 30, 2011

DC circuits

A simple resistor-capacitor circuit demonstrates charging of a capacitor.

A series circuit containing only a resistor, a capacitor, a switch and a constant DC source of voltage V₀ is known as a charging circuit.^[14] If the capacitor is initially uncharged while the switch is open, and the switch is closed at t = 0, it follows from Kirchhoff's voltage law that

$V_0= v_\text{resistor}(t) + v_\text{capacitor}(t) = i(t)R + \frac{1}{C}\int_0^t i(\tau)\mathrm{d}\tau.$

Taking the derivative and multiplying by C, gives a first-order differential equation,

$RC\frac{\mathrm{d}i(t)}{\mathrm{d}t} + i(t) = 0.$

At t = 0, the voltage across the capacitor is zero and the voltage across the resistor is V₀. The initial current is then i (0) =V₀ /R. With this assumption, the differential equation yields

$i(t)= \frac{V_0}{R} e^{\,^{\textstyle -t/\tau_0}}$