Q146 / 180 · COMEDK 2023 (Evening Shift) · Physics
$220 \mathrm{~V}$ ac is more dangerous than $220 \mathrm{~V}$ dc Why?
- AThe speed of ac is more than that of $\mathrm{dc}$
- BShock received from ac is always repulsive
- CThe frequency of ac is more than that of dc
- Correct answerDThe peak value of ac is greater than the given value of dc
Solution
The voltage specified for an alternating current (ac) circuit, such as $220 \mathrm{~V}$, refers to the root mean square (rms) value, denoted as $V_{rms}$.
The relationship between the peak value ($V_0$) and the rms value for a sinusoidal ac voltage is given by $V_0 = V_{rms} \sqrt{2}$.
Substituting the given value, $V_0 = 220 \sqrt{2} \approx 220 \times 1.414 \approx 311 \mathrm{~V}$.
In contrast, for a direct current (dc) source of $220 \mathrm{~V}$, the voltage remains constant at $220 \mathrm{~V}$ at all times.
Since the peak voltage of the ac supply ($311 \mathrm{~V}$) is significantly higher than the constant voltage of the dc supply ($220 \mathrm{~V}$), the ac supply is more dangerous as it can cause a higher potential difference across the body during the peak of the cycle.
Answer: The peak value of ac is greater than the given value of dc
The relationship between the peak value ($V_0$) and the rms value for a sinusoidal ac voltage is given by $V_0 = V_{rms} \sqrt{2}$.
Substituting the given value, $V_0 = 220 \sqrt{2} \approx 220 \times 1.414 \approx 311 \mathrm{~V}$.
In contrast, for a direct current (dc) source of $220 \mathrm{~V}$, the voltage remains constant at $220 \mathrm{~V}$ at all times.
Since the peak voltage of the ac supply ($311 \mathrm{~V}$) is significantly higher than the constant voltage of the dc supply ($220 \mathrm{~V}$), the ac supply is more dangerous as it can cause a higher potential difference across the body during the peak of the cycle.
Answer: The peak value of ac is greater than the given value of dc
Hence, the correct answer is option: 'D'.