In which of the following circumstances may the control operator of an amateur station receive compensation for operating that station?

The option stating that the communication is incidental to classroom instruction at an educational institution is correct because it aligns with the legal allowances for amateur radio operators. Amateur radio licenses are granted with the understanding that operators engage in non-commercial communication. Therefore, operating an amateur station for educational purposes, such as teaching students about radio technology or communication, does not constitute a violation of the rules regarding compensation, as the operator is not profiting from the communications but rather is fulfilling a role in an educational context.

Other scenarios mentioned in the choices present circumstances that would likely lead to a violation of amateur radio regulations. For instance, receiving compensation for communications related to the sale of equipment or for obtaining emergency information for a local broadcast station typically involves commercial operations, which are prohibited under amateur radio regulations. The distinction between educational use and commercial exploitation is crucial in understanding why the correct answer pertains specifically to educational contexts.