In the square wave below, E = 2V, what is the effective voltage? (your answer should be in volts to 2 decimal places)

1. Break Down the Problem

To find the effective voltage (also known as the root mean square or RMS voltage) of a square wave, we need to understand the properties of the square wave:

• The square wave oscillates between two levels (in this case, 0V and 2V).
• The effective voltage for a square wave can be calculated using the formula for RMS voltage.

2. Relevant Concepts

For a square wave: $V_{\text{rms}} = V_{\text{peak}} \cdot \frac{1}{\sqrt{2}}$ Where:

• $V_{\text{peak}} = 2V$

3. Analysis and Detail

Substituting $V_{\text{peak}}$ into the RMS voltage formula, we have: $V_{\text{rms}} = 2V \cdot \frac{1}{\sqrt{2}}$ Calculating $\frac{1}{\sqrt{2}}$: $\frac{1}{\sqrt{2}} \approx 0.7071$ Thus, $V_{\text{rms}} = 2V \cdot 0.7071 \approx 1.4142V$

4. Verify and Summarize

Rounding 1.4142V to two decimal places, we have: $V_{\text{rms}} \approx 1.41V$

Final Answer

The effective voltage is 1.41 volts.