Presentation on theme: "Alternating Current Circuits"— Presentation transcript:
1 Alternating Current Circuits Chapter 4Alternating Current Circuits
2 AC CircuitAn AC circuit consists of a combination of circuit elements and an AC generator or sourceThe output of an AC generator is sinusoidal and varies with time according to the following equationΔV = ΔVmax sin 2ƒtΔv is the instantaneous voltageΔVmax is the maximum voltage of the generatorƒ is the frequency at which the voltage changes, in HzSame thing about the current (if only a resistor)I = Imax sin 2ƒt
3 Resistor in an AC Circuit Consider a circuit consisting of an AC source and a resistorThe graph shows the current through and the voltage across the resistorThe current and the voltage reach their maximum values at the same timeThe current and the voltage are said to be in phaseVoltage varies asΔV = ΔVmax sin 2ƒtSame thing about the currentI = Imax sin 2ƒt
4 More About Resistors in an AC Circuit The direction of the current has no effect on the behavior of the resistorThe rate at which electrical energy is dissipated in the circuit is given byP = i2 R = (Imax sin 2ƒt)2 Rwhere i is the instantaneous currentthe heating effect produced by an AC current with a maximum value of Imax is not the same as that of a DC current of the same valueThe maximum current occurs for a small amount of timeAveraging the above formula over one cycle we get
5 rms Current and Voltage The rms current is the direct current that would dissipate the same amount of energy in a resistor as is actually dissipated by the AC currentAlternating voltages can also be discussed in terms of rms values
6 Ohm’s Law in an AC Circuit rms values will be used when discussing AC currents and voltagesAC ammeters and voltmeters are designed to read rms valuesMany of the equations will be in the same form as in DC circuitsOhm’s Law for a resistor, R, in an AC circuitΔVrms = Irms RAlso applies to the maximum values of v and i
7 Example: an AC circuitAn ac voltage source has an output of DV = 150 sin (377 t). Find(a) the rms voltage output,(b) the frequency of the source, and(c) the voltage at t = (1/120)s.(d) Find the maximum current in the circuit when the generator is connected to a 50.0W resistor.
8 Capacitors in an AC Circuit Consider a circuit containing a capacitor and an AC sourceThe current starts out at a large value and charges the plates of the capacitorThere is initially no resistance to hinder the flow of the current while the plates are not chargedAs the charge on the plates increases, the voltage across the plates increases and the current flowing in the circuit decreases
9 More About Capacitors in an AC Circuit The current reverses directionThe voltage across the plates decreases as the plates lose the charge they had accumulatedThe voltage across the capacitor lags behind the current by 90°
10 Capacitive Reactance and Ohm’s Law The impeding effect of a capacitor on the current in an AC circuit is called the capacitive reactance and is given byWhen ƒ is in Hz and C is in F, XC will be in ohmsOhm’s Law for a capacitor in an AC circuitΔVrms = Irms XC
11 Inductors in an AC Circuit Consider an AC circuit with a source and an inductorThe current in the circuit is impeded by the back emf of the inductorThe voltage across the inductor always leads the current by 90°
12 Inductive Reactance and Ohm’s Law The effective resistance of a coil in an AC circuit is called its inductive reactance and is given byXL = 2ƒLWhen ƒ is in Hz and L is in H, XL will be in ohmsOhm’s Law for the inductorΔVrms = Irms XL
13 Example: AC circuit with capacitors and inductors A 2.40mF capacitor is connected across an alternating voltage with an rms value of 9.00V. The rms current in the capacitor is 25.0mA. (a) What is the source frequency? (b) If the capacitor is replaced by an ideal coil with an inductance of 0.160H, what is the rms current in the coil?