Question: The voltage V produced by an ac generator is sinusoidal. As a function of time, the voltage V is V(t) = V 0 sin(2 ft)

The voltage V produced by an ac generator is sinusoidal. As a function of time, the voltage V is

V(t) = V₀ sin(2π ft)

where f is the frequency, the number of complete oscillations (cycles) per second. [In the United States and Canada, f is 60 hertz (Hz).] The power P delivered to a resistance R at any time t is defined as

[V(t)]² P(t) = R

(a) Show that

P(t) sin°(2¬ft).

(b) The graph of P is shown in the figure. Express P as a sinusoidal function.

[V(t)] P(t) = R P(t) sin(2ft).

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