Change: First Order Circuits

S contains m1, m2 and m3
m1 = voltage source, 100 V; m2 = 4 μF capacitor with initial charge, 800 μF;
m3 = Resistor, 10 Ω

First Order Circuit

Figure 7.25 is a RC circuit. The switch, S is closed at t = 0.

Determine the current i and capacitor charge, for t > 0.

Containership: The Complex Plane

S contains the space s1 which contains the point p.
S = Earth; s1 = circular complex plane with radius r (fig. 2.14 (b)).

Complex Plane

What is the complex coordinate of p?

Motion: Random Signals

S contains m
S = Earth; m = a signal source.

The signal v(t) from m is a binary waveform. It is either 0.5 V or -0.5 V. The sign change has a 50-50 chance of occurrence within the interval of 1 μs. In other words, v(t) has an equal chance for positive or negative values within this interval.
What is the average and effective values of v(t) over a period of 5 secs?

Forcce: Voltage Across RL In Series

S containsm1, m2, m3
S = Earth; m1 = voltage source, vs; m2 = Resistance, 5 Ω;
m3 = Inductor, 10 H.

RL Series Circuit

Figure 6.30(a) is a RL series circuit. Figure 6.29(b) shows the current through the circuit.
If T = 1 s, what is the voltage across RL?

Motion: Periodic Pulse

S containsm1, m2
S = Earth; m1 and m2 are signal sources.

Periodic Pulse

Figure 6.29(a) shows the periodic pulse v1(t) of m1 while figure 6.29(b) shows the periodic pulse v2 of m2.

What is the average and effective values of v1(t) and v2(t)?

Motion: Sinusoidal Waveforms

S contains m.
S = Earth; m = signal source.

Sinusoids

Figure 6.23 is the sinusoidal waveform of m. It is expressed as:

v(t) = A + Bsin(ωt + θ)----(1)

(a) Determine the values of A, B, ω and θ.
(b) The average and effective values of v(t).

Motion: Periodic Signals

S contains m.
S = Earth; m = signal source.

Sinusoids

Figure 2.13 shows two sinusoids (red, blue) representing the periodic signals of m.
(a) Which signal is a cosine function and which is a sine function?. Write the general form of the signals
(b) Express the cosine signal as a sine signal and the sine signal as a cosine signal.

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