What is the resistance of a 7 W light bulb connected to a 7 V battery source. The answer key says. 39 but not sure how they got that?

Power is current times voltage.

P = IV

And from Ohm's law, voltage is current times resistance.

V = IR

So if we solve for I in Ohm's law and substitute into the power equation:

I = V/R

P = (V/R) V

P = V² / R

Given that P = 7 W and V = 7 V:

7 = 7² / R

R = 7 Ω

Make sure you copied the problem correctly. If you did, the answer key may be wrong.