[amp_mcq option1=”0.5 of peak value” option2=”0.707 of peak value” option3=”Same as peak value” option4=”Zero” correct=”option2″]
The correct answer is B. 0.707 of peak value.
The root mean square (RMS) value of a function is defined as the square root of the average of the squared values of the function. For a pure cosine function, the RMS value is equal to 0.707 of the peak value. This can be shown by considering the following equation:
$$V(t) = V_m \cos(\omega t)$$
where $V_m$ is the peak value of the function and $\omega$ is the angular frequency. The RMS value of this function is given by:
$$V_{RMS} = \sqrt{\frac{1}{T} \int_0^T V^2(t) dt} = \sqrt{\frac{1}{T} \int_0^T V_m^2 \cos^2(\omega t) dt} = \sqrt{\frac{V_m^2}{2}} = 0.707 V_m$$
Therefore, the RMS value of a pure cosine function is equal to 0.707 of the peak value.
Option A is incorrect because the RMS value is not equal to 0.5 of the peak value. Option C is incorrect because the RMS value is not equal to the peak value. Option D is incorrect because the RMS value is not equal to zero.