https://file.aiquickdraw.com/mathbot/file/1727314529728f6b6zdb3.jpg

The question asks: 

**"What peak value of a.c. voltage would be required to produce the same heating effect as 100Vdc?"**

The relationship between the peak value of an AC voltage (\( V_{\text{peak}} \)) and the corresponding DC voltage that produces the same heating effect can be derived from the root mean square (RMS) voltage of the AC supply. The formula that connects the RMS voltage to the peak voltage is:

\[
V_{\text{RMS}} = \frac{V_{\text{peak}}}{\sqrt{2}}
\]

The heating effect of an AC voltage is equivalent to the heating effect of the RMS value of that AC voltage. In this case, the DC voltage given is 100 V, which is equivalent to the RMS value of the AC voltage. Therefore:

\[
100 = \frac{V_{\text{peak}}}{\sqrt{2}}
\]

Solving for \( V_{\text{peak}} \):

\[
V_{\text{peak}} = 100 \times \sqrt{2} \approx 141.42 \, \text{V}
\]

The answer written in the image is 200 V, which appears to be incorrect unless specified differently by the problem. The correct peak value is approximately **141.42 V**.

Would you like further clarification or details on any step?

### Related Questions:
1. What is the formula to convert peak voltage to RMS voltage?
2. Why is RMS voltage used when calculating heating effects in AC circuits?
3. How does the heating effect of a 200V peak AC voltage compare to a 100V DC voltage?
4. Can AC voltage ever produce a higher heating effect than the same DC voltage?
5. How do we calculate the heating effect of an AC current?

**Tip:** Always remember that the RMS value represents the effective value for AC when it comes to power and heating effects, as it's equivalent to DC for these calculations.

What peak value of a.c. voltage would be required to produce the same heating effect as 100Vdc?

Find out how to calculate the peak value of an AC voltage needed to produce the same heating effect as a 100V DC voltage. This problem involves key concepts in alternating current, root mean square (RMS) voltage, and the relationship between AC and DC for heating effects. Suitable for students in Grades 9-12.

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