| Contents for this page | Related topics |  |
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Resistive AC circuit Capacitive AC circuit Inductive AC circuit Impedance of an AC circuit Additional questions |
Heating effects of electric currents Inductive circuits Electric machines Alternating currents Alternating currents and safety |
 Data Glossary |
| Learning Outcomes | ||
| After studying this section, you will (a) be familiar with the basic principles underlying resistive, capacitive and inductive circuits, and (b) understand what is meant by the "impedance" of a circuit. | ||
The material in this section is at a higher level than is expected of South African Grade 12 learners, and is included here for the benefit of educators.
A resistive AC circuit is a simple circuit, containing an AC source and one or more resistors. The diagram on the right shows such a circuit. The voltage, E, at any time t will vary according to where Eo is the peak voltage (voltage amplitude) and the current I will vary similarly |
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As we can see from the diagram on the left, the current and the voltage are in phase, that is, the current I will be at its highest (or lowest) value when the voltage E is at its highest or lowest value.
This means that we can treat a purely resistive AC circuit in the same way as DC circuits are treated, particularly in the use of Ohm's law for resistors in series and parallel. |
A purely capacitive AC circuit is an AC circuit containing a AC voltage supply and a capacitor, C, such as the circuit shown here on the right.
A current will flow through the circuit, first in one direction, then in the other. However, no current actually flows through the capacitor. Electrons build up on the one plate and are drained off from the other plate in very rapid succession, giving the impression that the current flows through the insulator separating the plates. However, a capacitor in an AC circuit does offer resistance to the overall current flow. We define a quantity called the CAPACITIVE REACTANCE, X |
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where f is the frequency of the current, and C the capacitance of the capacitor in farads.The unit of capacitive reactance is, as is the case with resistance, the ohm.
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As we can see from the diagram on the left, the current and the voltage are not in phase, that is, the current I "leads" the voltage by 90º (the peaks of the current are 90º ahead of the peaks of the voltage) . Since at any time there will be a current flowing into one plate of the capacitor, and an equal and opposite current flowing out of the other plate, a current appears to flow through the capacitor. The reactance of the capacitor is treated as if it were a resistance, as shown in the worked example below. |
A purely inductive AC circuit is one that contains a voltage source across an inductor, L, such as the circuit shown here on the right. We define a quantity called the INDUCTIVE REACTANCE, XL of the inductor such that
where f is the frequency of the current, and L the inductance of the inductor in henrys. The unit of inductive reactance is the ohm. We see from the above formula that the inductive reactance is inversely proportional to the capacitance. In other words, the greater the capacitance of a capacitor in an AC circuit, the easier it is for the current to appear to flow through it. |
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As we can see from the diagram on the left, as in the case of a capacitive circuit, the current and the voltage are not in phase in phase. In the inductive case however, it is the voltage that "leads" the current by 90º (the peaks of the voltage are 90º ahead of the peaks of the current) . The reactance of the inductor is treated as if it were a resistance, as shown in the worked example below. |
Typical circuits normally consist of a resistor and a capacitor (RC circuit), a resistor and an inductor (RL circuit) , or a resistor, inductor and capacitor (RLC circuit) in series. The combination of these elements offer an apparent resistance to the flow of current, called the IMPEDANCE, Z of the circuit. Impedance is measured in ohms. The impedance is a function of the resistance of the resistors and the reactances of the capacitor and/or inductor. The formulae connecting these quantities for the different types of circuits are shown in the table below.
| Circuit type | Impedance, Z |
|---|---|
| RC |  |
| RL |  |
| RLC |  |
The impedance of an AC circuit is the ratio of the root mean square voltage and the root mean square current:
