A

Given Data:
- Inductance (L) = 0.10 H
- Capacitance (C) = 25.0 μF = 25.0 \times 10^{-6} F
- Resistance (R) = 25.0 Ω
- EMF (E) = 310 sin(314t) V

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

Step 2: Find the Reactance of the Circuit
- Inductive Reactance \( X_L = \omega L = 314 \times 0.10 = 31.4 \, \Omega \)
- Capacitive Reactance \( X_C = \frac{1}{\omega C} = \frac{1}{314 \times 25.0 \times 10^{-6}} \approx 12.74 \, \Omega \)

Step 3: Find the Total Reactance
The total reactance (X) is given by:
\( X = X_L - X_C = 31.4 - 12.74 = 18.66 \, \Omega \)

Step 4: Find the Impedance of the Circuit
The impedance (Z) is given by:
\( Z = \sqrt{R^2 + X^2} = \sqrt{25.0^2 + 18.66^2} \approx 30.29 \, \Omega \)

Step 5: Calculate the Current in the Circuit
From Ohm's law, the current (I) can be found as:
\( I = \frac{E_0}{Z} = \frac{310}{30.29} \approx 10.23 \, A \)

Step 6: Find the Phase Angle
The phase angle (\( \phi \)) can be calculated using:
\( \tan\phi = \frac{X}{R} = \frac{18.66}{25} \Rightarrow \phi = \tan^{-1}\left(\frac{18.66}{25}\right) \approx 38.0^{\circ} \)

Step 7: Find Effective Voltage Across Components
- Voltage across Resistor (V_R): \( V_R = I \cdot R = 10.23 \times 25 \, \approx 255.75 \, V \)
- Voltage across Inductor (V_L): \( V_L = I \cdot X_L = 10.23 \times 31.4 \approx 321.35 \, V \)
- Voltage across Capacitor (V_C): \( V_C = I \cdot X_C = 10.23 \times 12.74 \approx 130.02 \, V \)

Summary:
(i) Frequency = 50 Hz
(ii) Reactance = 18.66 Ω
(iii) Impedance = 30.29 Ω
(iv) Current = 10.23 A
(v) Phase angle = 38.0°
Effective Voltages: V_R ≈ 255.75 V, V_L ≈ 321.35 V, V_C ≈ 130.02 V.