31. Alternating Current

An AC source operates with a 0.05 s period. 0.025 s after the current is at a maximum, the current is measured to be 1.4 A. What is the RMS current of this AC circuit?

You have a special light bulb with a very delicate wire filament. The wire will break if the current in it ever exceeds 1.50 A, even for an instant. What is the largest root-mean-square current you can run through this bulb?

Off to Europe! You plan to take your hair dryer to Europe, where the electrical outlets put out 240 V instead of the 120 V seen in the United States. The dryer puts out 1600 W at 120 V. What could you do to operate your dryer via the 240 V line in Europe?

Off to Europe! You plan to take your hair dryer to Europe, where the electrical outlets put out 240 V instead of the 120 V seen in the United States. The dryer puts out 1600 W at 120 V. (b) What current will your dryer draw from a European outlet? (c) What resistance will your dryer appear to have when operated at 240 V?

You're the operator of a 15,000 V rms, 60 Hz electrical substation. When you get to work one day, you see that the station is delivering 6.0 MW of power with a power factor of 0.90. What is the rms current leaving the station?

Commercial electricity is generated and transmitted as three-phase electricity. Instead of a single emf, three separate wires carry currents for the emfs ε₁ = ε₀ cos ωt, ε₂ = ε₀ cos(ωt +120°), and ε₃ = ε₀ cos(ωt−120°) over three parallel wires, each of which supplies one-third of the power. This is why the long-distance transmission lines you see in the countryside have three wires. Suppose the transmission lines into a city supply a total of 450 MW of electric power, a realistic value. What would be the rms current in each wire if the transmission voltage were ε₀ = 120 V rms?

Commercial electricity is generated and transmitted as three-phase electricity. Instead of a single emf, three separate wires carry currents for the emfs ε₁ = ε₀ cos ωt, ε₂ = ε₀ cos(ωt +120°), and ε₃ = ε₀ cos(ωt−120°) over three parallel wires, each of which supplies one-third of the power. This is why the long-distance transmission lines you see in the countryside have three wires. Suppose the transmission lines into a city supply a total of 450 MW of electric power, a realistic value. In fact, transformers are used to step the transmission-line voltage up to 500 kV rms. What is the current in each wire?

A motor attached to a 120 V/60 Hz power line draws an 8.0 A current. Its average energy dissipation is 800 W. What is the rms resistor voltage?

The voltage across the terminals of an ac power supply varies with time according to Eq. (31.1) v = Vcosωt. The voltage amplitude is V = 45.0 V. What are (a) the root-mean-square potential difference V_rms and (b) the average potential difference V_av between the two terminals of the power supply?

If the current gain of the transistor amplifier in Fig. 40–49 is β = i_c/i_B = 95, what value must R_c have if a 1.0-μA ac base current is to produce an ac output voltage of 0.40 V?

An amplifier has a voltage gain of 75 and a 25-kΩ load (output) resistance. What is the peak output current through the load resistor if the input voltage is an ac signal with a peak of 0.080 V?

(II) An ac voltage of 120 V rms is to be rectified. Estimate very roughly the average current in the output resistor R (42 kΩ) for (a) a half-wave rectifier (Fig. 40–39), and (b) a full-wave rectifier (Fig. 40–40) without capacitor.

(II) From Fig. 40–49, write an equation for the relationship between the base current (I_B), the collector current (I_c), and the emitter current (I_E), not labeled in Fig. 40–49). Assume the ac current i_B = i_C = 0.

Show that if the inductor L in the filter circuit of Fig. 30–33 (Problem 87) is replaced by a large resistor R, there will still be significant attenuation of the ac voltage and little attenuation of the dc voltage if the input dc voltage is high and the current (and power) are low.