A

Step 1: Find the Frequency of the EMF
Given the equation of emf is E = 310 sin(314t), the angular frequency \( \omega \) can be found where \( \omega = 314 \) rad/s.\
The frequency (f) can be calculated using the relation: \( f = \frac{\omega}{2\pi} = \frac{314}{2\pi} \approx 50 \) Hz.

Step 2: Calculate the Reactance of the Circuit
For the given components:
- Inductive reactance, \( X_L = \omega L = 314 \times 0.1 = 31.4 \; \Omega \)
- Capacitive reactance, \( X_C = \frac{1}{\omega C} = \frac{1}{314 \times 25 \times 10^{-6}} \approx 12.74 \; \Omega \)

Step 3: Calculate the Impedance of the Circuit
The total impedance (Z) in an RLC series circuit is given by:
\( Z = \sqrt{R^2 + (X_L - X_C)^2} \)
Substituting the values:
\( Z = \sqrt{(25)^2 + (31.4 - 12.74)^2} \approx \sqrt{625 + 339.76} \approx \sqrt{964.76} \approx 31.06 \; \Omega \)

Step 4: Calculate the Current in the Circuit
Using Ohm's law: \( I = \frac{E_{rms}}{Z} \), where: \( E_{rms} = \frac{E_{max}}{\sqrt{2}} = \frac{310}{\sqrt{2}} \approx 219.19 V \)
Thus: \( I = \frac{219.19}{31.06} \approx 7.05 A \)

Step 5: Calculate the Phase Angle
The phase angle (φ) can be calculated using:
\( \tan(\phi) = \frac{X_L - X_C}{R} \)
Substituting the known values:
\( \tan(\phi) = \frac{31.4 - 12.74}{25} = \frac{18.66}{25} \approx 0.7464 \rightarrow \phi = \tan^{-1}(0.7464) \approx 36.5° \)

Voltage calculations:
- Voltage across the resistor: \( V_R = I \cdot R = 7.05 \cdot 25 = 176.25 V \)
- Voltage across the inductor: \( V_L = I \cdot X_L = 7.05 \cdot 31.4 \approx 221.07 V \)
- Voltage across the capacitor: \( V_C = I \cdot X_C = 7.05 \cdot 12.74 \approx 89.78 V \)

Thus, overall results are:
- Frequency: 50 Hz,
- Reactance: Inductive \( X_L = 31.4 \; \Omega, X_C = 12.74 \; \Omega \),
- Impedance: \( Z \approx 31.06 \; \Omega \),
- Current: \( I \approx 7.05 A \),
- Phase Angle: \( \phi \approx 36.5° \),
- Voltages: \( V_R \approx 176.25 \, V, V_L \approx 221.07 \, V, V_C \approx 89.78 \, V \).