Chapter 30 Inductance, Electromagnetic Oscillations, and AC Circuits
30-7 AC Circuits with AC Source Resistors, capacitors, and inductors have different phase relationships between current and voltage when placed in an ac circuit. The current through a resistor is in phase with the voltage.
30-7 AC Circuits with AC Source The voltage across the inductor is given by or. Therefore, the current through an inductor lags the voltage by 90.
30-7 AC Circuits with AC Source The voltage across the inductor is related to the current through it:. The quantity X L is called the inductive reactance, and has units of ohms:
30-7 AC Circuits with AC Source Example 30-9: Reactance of a coil. A coil has a resistance R =100Ω 1.00 Ω and an inductance of 0.300 H. Determine the current in the coil if (a) 120-V dc is applied to it, and (b) 120-V ac (rms) at 60.0 Hz is applied. Solution p797
30-7 AC Circuits with AC Source The voltage across the capacitor is given by. Therefore, in a capacitor, the current leads the voltage by 90.
30-7 AC Circuits with AC Source The voltage across the capacitor is related to the current through it:. The quantity X C is called the capacitive reactance, and (just like the inductive reactance) has units of ohms:
30-7 AC Circuits with AC Source Example 30-10: Capacitor reactance. What is the rms current in the circuit shown if C = 1.0 μf and V rms = 120 V? Calculate (a) for f = 60 Hz and then (b) for f = 6.0 x 10 5 Hz. Solution p799
30-7 AC Circuits with AC Source This figure shows a high-pass filter (allows an ac signal to pass but blocks a dc voltage) and a low-pass filter (allows a dc voltage to be maintained but blocks higher-frequency fluctuations). ti
30-8 LRC Series AC Circuit Analyzing the LRC series AC circuit is complicated, as the voltages are not in phase this means we cannot simply add them. Furthermore, the reactances depend on the frequency.
30-8 LRC Series AC Circuit We calculate the voltage (and current) using what are called phasors these are vectors representing the individual voltages. Here, at t =0 0, the current and voltage are both at a maximum. As time goes on, the phasors will rotate counterclockwise.
30-8 LRC Series AC Circuit Some time t later, the phasors have rotated.
30-8 LRC Series AC Circuit The voltages across each device are given by the x-component t of each, and the current by its x-component. The current is the same throughout the circuit.
30-8 LRC Series AC Circuit We find from the ratio of voltage to current that the effective resistance, called the impedance, of the circuit is given by
30-8 LRC Series AC Circuit The phase angle between the voltage and the current is given by or The factor cos φ is called the power factor of the circuit.
30-8 LRC Series AC Circuit Example 30-11: LRC circuit. Suppose R = 25.0 Ω, L = 30.0 mh, and C = 12.0 μf, and they are connected in series to a 90.0-V ac (rms) 500-Hz source. Calculate (a) the current in the circuit, (b) the voltmeter readings (rms) across each element, (c) the phase angle φ, φ and (d) the power dissipated in the circuit. Solution p801
30-9 Resonance in AC Circuits The rms current in an ac circuit is Clearly, l I rms depends d on the frequency.
30-9 Resonance in AC Circuits We see that I rms will be a maximum when X C = X L ; the frequency at which this occurs is f 0 = ω 0 /2π is called the resonant frequency.