Question

The wattage of a bulb is 24W when it is connected to a 12 v battery. Calculate the effective wattage if it operates on 6v battery. Calculate the wattage if it operates on a 6 v battery.
Which of the following solution is correct for the above question and why and how to know which way to do?

Solution 1:-
P=V*I
I=P/V
I=24/12
I=2 A
Now V = 6v
New P = V*I = 6*2 = 12W

Solution 2:-
P = V^{​​​​​​2}/R
R = V^{​​​​​​2}/P
R = 12²/24
R = 6 Ohm

Now V = 6v
New P = V²/R = 6²/6 = 6W

Answer 1

The second answer will be correct.because in the first one,we find the current at the supply of 12 volt and use it to find the power at 6v.but we should think that the current at 12v and 6v is not the same.

but in the second case, we are finding the resistance,which is always same for the bulb.so we can use it to find the power.