If the current from the source in Example 12 is i = 5 cos4t and the diode

If the current from the source in Example 12 is i = 5 cos4πt and the diode allows only negative current to flow, write the inequalities and draw the graph for the current in the circuit as a function of time for 0 ≤ t ≤ 1 s.

Data from Example 12

A semiconductor diode has the property that an electric current flows through it in only one direction. If it is an alternating-current circuit, the current in the circuit flows only
during the half-cycle when the diode allows it to flow. If a source of current given by i = 2 sinπt (i in mA, t in seconds) is connected in series with a diode, write the inequalities for the current and the time. Assume the source is on for 3.0 s and a positive current passes through the diode.

We are to find the values of t that correspond to i > 0. From the properties of the sine function, we know that 2 sinπt has a period of 2π/π = 2.0 s. Therefore, the current is zero for t = 0, 1.0 s, 2.0 s, and 3.0 s. The source current is positive for 0 < t < 1.0 s and for 2.0 s < t < 3.0 s. The source current is negative for 1.0 s < t < 2.0 s. Therefore, in the circuit

A graph of the current in the circuit as a function of time is shown in Fig. 17.6(a). In Fig. 17.6(b), the values of t for which i > 0 are shown.

Transcribed Image Text:

i> 0 for 0 < t < 1.0 s and 2.0 s < t < 3.0 s i = 0 for t = 0, 1.0 s < t < 2.0 s