C

Step 1: Understand the scenario involving the rotation of the ring and the behavior of the magnetic needle. When the ring rotates, the small magnetic needle will experience a change in magnetic field due to the induced electromotive force (emf) because of the motion of the ring in Earth's magnetic field.

Step 2: The average angle α at which the needle deviates relates to the induced emf in the ring. For a circular loop rotating in a magnetic field, the induced emf (E) can be given by the formula:
$$ E = Bvl $$
where B is the magnetic field strength, v is the linear velocity, and l is the effective length.

Step 3: Determine the linear velocity (v). For a circular ring rotating with angular velocity (ω), the linear velocity is given as:
$$ v = ext{R} imes ext{ω} $$
Given that ω = 10 turns/second, we convert it into rad/s:
$$ ext{ω} = 10 imes 2 ext{π} ext{ rad/s} $$
Thus:
$$ v = R imes (20 ext{π}) $$

Step 4: Next, the induced emf can also be related to the resistance (R) in the circuit formed by the ring and the current (I) using Ohm's law:
$$ E = IR $$

Step 5: Substitute E in the Ohm's law with the expression from step 2. We set up:
$$ B imes (R imes 20 ext{π}) imes l = I R $$
Rearranging gives us:
$$ R = \frac{B imes (R imes 20 ext{π}) imes l}{I} $$

Step 6: The final answer for R will depend on known quantities such as B (magnetic field strength), l (effective length), and I (current). Thus, the answer would be based on these computations.
Therefore, the electrical resistance R of the ring is expressed as ultimately dependent on the change in the magnetic field and motion of the ring, correlating to the angle α of deviation.