A battery of voltage V delivers power P to a resistor of resistance R connected to it. By what factor will the power delivered to the resistor change if the following changes are made? Give your answers as a factor of the original power P. (a) The resistance is changed to 2.90R. (b) The voltage of the battery is now 2.90V, but the resistance is R. (c) The resistance is 2.90R and voltage is 2.90V. (d) The resistance is 2.90R and the voltage is V/2.90.

Power P = V² / R

a) The resistance is changed to 2.90R

Power will become 1 / 2.9 times.

b) The voltage of the battery is now 2.90V, but the resistance is R

P = (2.9V) ² / R

= 8.41 x V² / R

So power becomes 8.41 times

c) The resistance is 2.90R and voltage is 2.90V

Power P = (2.9V) ² / 2.9 R

= 2.9 V²/R

So power becomes 2.9 times

d) The resistance is 2.90R and the voltage is V/2.90

Power P = (V/2.90) ² x 1 / 2.90R

1 / (2.9) ³ x V² / R

= 1 / 24.389 x V² / R

So power becomes 1 / 24.389 times.