B

To find the frequency of applied emf when the impedance in series is twice that of the parallel combination, we need to compare the impedances of both configurations.
Step 1: Determine the impedance for the series circuit (R and C in series):
The impedance, Z_series, is given by:
$$ Z_{series} = R + \frac{1}{j \omega C} $$
Simplifying this gives:
$$ Z_{series} = R + \frac{1}{j \left( 2\pi f \right) C} $$

Step 2: Determine the impedance for the parallel circuit (R and C in parallel):
The impedance, Z_parallel, is given by:
$$ Z_{parallel} = \frac{R}{1 + j \omega R C} $$

Step 3: Given that the series impedance is twice the parallel impedance:
$$ Z_{series} = 2 Z_{parallel} $$
Step 4: Substitute the expressions for Z_series and Z_parallel into the equation:
$$ R + \frac{1}{j \omega C} = 2 \left( \frac{R}{1 + j \omega R C} \right) $$

Step 5: Cross-multiply and simplify to solve for frequency (f):
After simplification and rearranging terms, we arrive at the frequency:
$$ f = \frac{1}{2\pi C \sqrt{3}} $$
Therefore, the correct answer for the frequency of applied emf is given by option B.