C

To find the RMS and average value of the given waveform, we follow these steps:
Step 1: Identifying waveform characteristics
The waveform is triangular in shape. The positive half oscillates between 0 and maximum value (yE) and the negative half oscillates from maximum value to a minimum of 0.
Step 2: Calculating the average value (V_avg)
The average value of a triangular wave can be calculated using the formula:
$$ V_{avg} = \frac{1}{T} \int_0^T V(t) dt $$
For a triangular wave with a peak value of yE:
$$ V_{avg} = \frac{2 \cdot yE}{3} $$
Step 3: Calculating the RMS value (V_rms)
The RMS value is derived as follows for a triangular wave:
$$ V_{rms} = \frac{V_{peak}}{\sqrt{3}} = \frac{yE}{\sqrt{3}} $$
Step 4: Conclusion
Thus, the average value is \(\frac{2}{3} yE\) and the RMS value is \(\frac{yE}{\sqrt{3}}\). Therefore, the answer options match with C.