In this lab we study a simple circuit with a resistor and a capacitor from two points of view, one in time and the other in frequency. The viewpoint in time is based on a differential equation. The equation shows that the RC circuit is an approximate integrator or approximate differentiator. The viewpoint in frequency sees the RC circuit

as a filter, either low-pass or high-pass.

(a) A voltage-step forcing function is shown as the source driving a general network. (b) A simple circuit which, although not the exact equivalent of part (a), may be used as its equivalent in many cases. (c) An exact equivalent of part (a).

The impedance of an RL circuit is the total opposition to AC current flow caused by the resistor (R) and the reactance of the inductor (XL).

When we applied a dc voltage to a resistor and capacitor in series, the capacitor charged to the applied voltage along an exponential curve, and then just sat there. This is not the case when an ac voltage is applied to this combination as shown in the schematic diagram to the right. Here, the input voltage is constantly changing, so the capacitor will constantly charge and discharge as it continually tries to oppose the changes.

A video presentation about resistor-capacitor circuits that are connected in parallel.

The parallel RC circuit shown to the right behaves very differently when AC is applied to it, than when DC is applied. With a DC voltage, the capacitor will charge rapidly to that voltage, after which the only current flowing will be through the resistor. But with an applied AC voltage, the capacitor cannot ever reach a final charge, and therefore will always be carrying some current.

Parallel AC circuits exhibit the same fundamental properties as parallel DC circuits: voltage is uniform throughout the circuit, branch currents add to form the total current, and impedances diminish (through the reciprocal formula) to form the total impedance.

Finding the impedance of a parallel RLC circuit is considerably more difficult than finding the series RLC impedance. This is because each branch has a phase angle and they cannot be combined in a simple way. The impedance of the parallel branches combine in the same way that parallel resistors combine:

An RLC circuit (or LCR circuit) is an electrical circuit consisting of a resistor, an inductor, and a capacitor, connected in series or in parallel. The RLC part of the name is due to those letters being the usual electrical symbols for resistance, inductance and capacitance respectively. The circuit forms a harmonic oscillator for current and will resonate in just the same way as an LC circuit will. The difference that the presence of the resistor makes is that any oscillation induced in the circuit will die away over time if it is not kept going by a source. This effect of the resistor is called damping. Some resistance is unavoidable in real circuits, even if a resistor is not specifically included as a component. A pure LC circuit is an ideal which really only exists in theory.

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