RC Circuit Principles

Discussion of Principles

RC Circuits

A capacitor is a device for storing charge. The ability of a capacitor to hold a charge is measured by its capacitance C. For a capacitor, Q = CV, where Q is the charge on one of the capacitor plates, C is the capacitance of the capacitor, and V is the potential difference maintained across the capacitor plates. The unit of capacitance is the Farad (F), where one Farad equals one Coulomb per volt (1F = 1C/V).

If a capacitor is connected to a battery, it will cause a charge +Q to develop on one plate and a charge -Q to develop on the other. If the battery is removed from the circuit the capacitor is connected to a resistor, then the capacitor will discharge through the resistor. The voltage across the resistor is given by V = IR, where I is the current through the resistor at a given time, and R is the resistance of the resistor. Since V = Q/C, = we can also write

I = V/R = Q/RC

As the capacitor discharges, Q becomes smaller, and I also becomes smaller.

The current at any time t is given by:

I = I₀e^-t/RC = I₀e^-t/τ

where I0 = initial value of the current, ti = time elapsed in seconds since the discharging began, τ = RC = capacitive time constant for the RC circuit, and e = 2.71828... .

A plot of I versus t is shown on the left below. This plot is an exponential decay curve. The current in the RC circuit exponentially decays over time. If we plot the natural logarithm (ln) of the ratio I/I0, the graph (seen on the right below) becomes a straight line whose slope is -1/τ.