How Does Voltage Variation Affect Power in a 100-W Heater?

[LeakyFrog]

Homework Statement

A 100-W heater is designed to operate with an applied
voltage of 120V.

a) What is the heater's resistance, and what current does the heater carry?

b) Show that if the potential difference V across the heater changes by a small
amount ΔV, the power P changes by a small amount ΔP, where ΔP/P = 2ΔV/V. (Hint:
Approximate the changes by modeling them as differentials, and assume the
resistance is constant.

c) Using the part b result, find the approximate power delivered to the heater
if the potential difference is decreased to 115V. Compare your result to the
exact answer.

Homework Equations

P = IV = V²/R

The Attempt at a Solution

I'm stuck on part b). So far I have
ΔP=ΔV²/R

ΔP/P=(ΔV/V)²

I'm not really sure what to do.

 

[ehild]

The change of a function f(x) can be approximated by Δf=f'(x)Δx, where f' is the derivative of f(x) taken at the original value of x, and Δx is a small change of x.


ehild

 

[LeakyFrog]

Thanks.

Another question, for part c) when you change the voltage on a circuit does the resistance stay the same? Or the current? Although I don't really see how the current could but maybe i suppose.

 

[ehild]

The heater stays the same, isn't it? And it consist of a resistor, and some other parts which do not change either, if you plug it into an other socket or the household voltage decreases because of some overload happening in the network.
Question c. wants you to apply the formula in question b, if V and ΔV are given.

ehild