B

To find the voltage developed in the secondary coil of the transformer, we can use the transformer equation:
\\frac{V_p}{V_s} = \\frac{N_p}{N_s}
where:
- \( V_p \) is the primary voltage
- \( V_s \) is the secondary voltage
- \( N_p \) is the number of turns in the primary coil
- \( N_s \) is the number of turns in the secondary coil

Given:
- \( N_p = 500 \) turns
- \( N_s = 50 \) turns
- \( V_p = 100 \) volts

Plugging in the values, we get:
\( \frac{100}{V_s} = \frac{500}{50} \)
Simplifying the right side:
\( \frac{500}{50} = 10 \)
Thus,
\( \frac{100}{V_s} = 10 \)
Rearranging to find \( V_s \):
\( V_s = \frac{100}{10} = 10 \) volts
Therefore, the voltage developed in the secondary will be 10 volts.