https://file.aiquickdraw.com/mathbot/file/17259992945640wthwfcw.jpg

The problem asks for the **average value of the voltage signal** shown in the diagram.

We can calculate the average value of a periodic signal using the following formula:

\[
V_{\text{avg}} = \frac{1}{T} \int_0^T V(t) \, dt
\]

But for a piecewise constant signal, the average value can be simplified as:

\[
V_{\text{avg}} = \frac{V_1 \times t_1 + V_2 \times t_2}{T}
\]

Where:
- \( V_1 = +40 \, \text{V} \) for the duration of \( t_1 = 2.5 \, \text{ms} \) (the pulse width).
- \( V_2 = -20 \, \text{V} \) for the remaining time \( t_2 = T - t_1 = 10 \, \text{ms} - 2.5 \, \text{ms} = 7.5 \, \text{ms} \).
- \( T = 10 \, \text{ms} \) is the total period.

Now, let's plug in the values and calculate the average voltage:

\[
V_{\text{avg}} = \frac{(+40 \, \text{V}) \times (2.5 \, \text{ms}) + (-20 \, \text{V}) \times (7.5 \, \text{ms})}{10 \, \text{ms}}
\]

\[
V_{\text{avg}} = \frac{100 \, \text{Vms} - 150 \, \text{Vms}}{10 \, \text{ms}} = \frac{-50 \, \text{Vms}}{10 \, \text{ms}} = -5 \, \text{V}
\]

So, the average value of the voltage signal is \(-5 \, \text{V}\).

Would you like further clarification on this? Here are 5 questions that extend from this topic:

1. How is the average value of non-constant signals computed in general?
2. What is the difference between average and RMS (root mean square) voltage?
3. How do different signal shapes affect the average voltage value?
4. How does the period \( T \) influence the average voltage in periodic signals?
5. What is the physical significance of a negative average voltage?

**Tip**: For any periodic signal, the average voltage over a period \( T \) can help identify any DC offset in an alternating waveform.

Calculate the average value of the voltage signal below.

Learn how to calculate the average voltage of a piecewise constant periodic signal. The problem involves key concepts like signal processing, average value calculation, and the application of simple formulas. In this example, a signal alternating between 40V and -20V is analyzed over a 10 ms period.

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