What voltage would be measured across the 15 ohm resistor with a 10V battery?

That depends on what other components are in the same circuit

along with the 15-ohm resistor.

If there's nothing else, and the battery is connected across the 15-ohm

resistor, then when you measure the voltage across the 15-ohm resistor,

your voltmeter is also connected straight across the battery, and you read

10 volts.

6.667 watts 0.667 Amps