B

To find the rms value of the given alternating emf $E = 8 \sin(\omega t) + 6 \sin(2\omega t)$ volts, we follow these steps:

Step 1: Identify the components of the EMF. The given emf consists of two sinusoidal components:
- First component: $E_1 = 8 \sin(\omega t)$
- Second component: $E_2 = 6 \sin(2\omega t)$

Step 2: Calculate rms for each component. The rms value for a sinusoidal waveform is given by the formula: $E_{rms} = \frac{E_{peak}}{\sqrt{2}}$.
- For the first component: $E_{1_{rms}} = \frac{8}{\sqrt{2}} = 4\sqrt{2}$
- For the second component: $E_{2_{rms}} = \frac{6}{\sqrt{2}} = 3\sqrt{2}$

Step 3: Calculate the total rms value. When combining rms values of independent sinusoidal sources: \( E_{total_{rms}} = \sqrt{E_{1_{rms}}^2 + E_{2_{rms}}^2} \) = \( \sqrt{(4\sqrt{2})^2 + (3\sqrt{2})^2} \)
= \( \sqrt{32 + 18} = \sqrt{50} = 5\sqrt{2} \)

Final answer: Therefore, the rms value of the alternating emf is $5\sqrt{2}$ volts.