Chapter 24 - Alternating-Current Circuits - Problems and Conceptual Exercises - Page 872: 98

(a) $\frac{V_{max}}{2}$ (b) $\frac {V_{max}}{\sqrt2}$

(a) We know that $V_{avg}=\frac{V_{max}(\frac{1}{2}t_{\circ})+(0)(\frac{1}{2}t_{\circ})}{t_{\circ}}=\frac{V_{max}}{2}$ (b) $V_{rms}=\sqrt{(V)^2_{avg}}=\sqrt{\frac{V_{max}^2(\frac{1}{2}t_{\circ})+(0)^2(\frac{1}{2}t_{\circ})}{t_{\circ}}}=\frac {V_{max}}{\sqrt2}$