1. **Problem Statement:** Define directivity and power gain of an antenna, and estimate power gain $G_p$ given $R_w = 10\Omega$, $R_{rad} = 0\Omega$, and directivity $D = 100$. 2. **Definitions:** - Directivity $D$ is the ratio of the radiation intensity in a given direction to the average radiation intensity over all directions. - Power gain $G_p$ of an antenna accounts for both directivity and efficiency, given by $G_p = D \times \eta$. 3. **Efficiency $\eta$:** Efficiency is the ratio of radiated power to total input power, expressed as $$\eta = \frac{R_{rad}}{R_{rad} + R_w}$$ where $R_{rad}$ is the radiation resistance and $R_w$ is the loss resistance. 4. **Given values:** - $R_w = 10\Omega$ - $R_{rad} = 0\Omega$ - $D = 100$ 5. **Calculate efficiency:** $$\eta = \frac{0}{0 + 10} = 0$$ 6. **Calculate power gain:** $$G_p = D \times \eta = 100 \times 0 = 0$$ 7. **Interpretation:** Since $R_{rad} = 0$, no power is radiated, so efficiency and power gain are zero despite high directivity. **Final answer:** $$G_p = 0$$