Sample problem: A 0.4-H inductor and a 220-Ω resistor are connected in
series to an ac generator with an rms voltage of 30 V and a frequency of 60 Hz.
Find the rms values of the current, voltage across the resistor, and voltage
across the inductor. What is the average power dissipation in the circuit?
Solution: Power dissipation (i.e., wasted heat) occurs only in the
resistor.
Sample problem: An ac generator with rms voltage of 110 V is connected
in series with a 35-W resistor and 1-μF
capacitor. At what frequency must the generator operate if it is to maintain a
current of 1.2 Amps.
Solution:
Z = V/I = 110/1.2 = 91.7 Ω
Z2 = R2 + (1/ ωC)2; f = ω/2π = 1.9 kHz
Sample problem: A typical "light dimmer" used to dim the stage lights
in a theater consists of a variable inductor L (whose inductance is adjustable
between zero and Lmax) connected in series with a light bulb. The
electrical supply is 120 V (rms) at 60 Hz; the light bulb is rated as "120 V, 900
W.“ What Lmax is required if the rate of energy dissipation in the
light bulb is to be varied from its minimum of 180 W to its upper limit of 900 W?
Assume that the resistance of the light bulb is independent of its temperature.
Solution:
Sample problem: An ac generator emf is ε = ε0∙sinωt, with ε0
= 22.8 V and ω = 353 rad/s. It is connected to a 17.3 H inductor. When the
current is at its maximum, what is the emf of the generator? When the emf of the
generator is -11.4 V and increasing in magnitude, what is the current?
Solution: The key point here is that the current has the same sinusoidal
behavior as the emf but lags the emf by 90º.
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