Lab217 - RC Circuits

Lab217 - RC Circuits - Samuel Dzifanu Lab 217 RC Circuits...

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Samuel Dzifanu Lab 217: RC Circuits RC Circuits Name : Samuel Dzifanu Objective: To observe and analyze the voltage as a function of time across a capacitor in a circuit containing a resistor and capacitor connected in series. Theory: When a capacitor is charged through a resistor by a DC voltage source, the charge in the capacitor and the voltage across the capacitor will increase with time. The voltage V as a function of time t is given by: V(t) = Vs(1 - e^(-t/RC)) and the charge: q(t) = qMax(1 - e^(-t/RC)) with the exponential e = 2.718 as the base of natural logarithm and Vs as the voltage of the source . The quantity RC = τ (Tau) is known the time constant . The curve of the voltage rises during the charging process. At time t = τ =RC (one time constant), the voltage across the capacitor has grown to a value: V (t = RC) = V (1- e^-1 ) = V (1- 1/e) = 0.63 and after 5 time constants (5RC) the capacitor is almost fully charged with its voltage almost equal to the supply voltage (99.3%). We can reasonably say that the capacitor is fully charged after 5RC, although really charging continues for ever (or until the circuit is changed).

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