31. Alternating Current

An AC source produces an alternating current in a circuit with the function $i\left(t\right)=\left(1.5A\right)\cos\left\lbrack\left(250s^{-1}\right)t\right\rbrack$. What is the frequency of the source? What is the maximum current in the circuit?

The current in an AC circuit takes 0.02 s to change direction. What is the angular frequency of the AC source?

A sinusoidal current i = I cosωt has an rms value I_rms = 2.10 A. What is the current amplitude?

Suppose a current is given by the equation I = 1.40 sin 210t , where I is in amperes and t in seconds. What is the frequency?

Suppose a current is given by the equation I = 1.40 sin 210t, where I is in amperes and t in seconds. What is the rms value of the current?

Estimate how far can an average electron move along one of the connecting wires of a 750-W toaster during an alternating current cycle? The power cord has copper wires of diameter 1.7 mm and is plugged into a 60-Hz 120-V ac outlet. [Hint: For sinusoidal motion, Chapter 14, we saw that the maximum distance traveled from equilibrium (amplitude A) is proportional to the maximum (drift) speed (Eq. 14–9a). This maximum drift speed is related to the maximum current (Section 25–8), which is calculated as the first step here; see Chapter 14.]

In FIGURE P32.54, what is the current supplied by the emf when (a) the frequency is very small and (b) the frequency is very large?