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## Homework Statement

Some light-dimmer switches use a variable resistor as shown in figure. The slide moves from position x = 0 to x = 1, and the resistance up to slide position x is proportional to x (the total resistance is R

_{pot}= 100Ω at x = 1). What is the power expended in the light bulb if x = 0.5?

## Homework Equations

R

_{series}= R

_{1}+ R

_{2}+ ...

R

_{parallel}= 1 / (1 / R

_{1}+ 1 / R

_{2}+ ...)

P = V

^{2}/ R = I

^{2}R

## The Attempt at a Solution

I tried first to obtain the total resistance, which is 50 + 1 / (1 / 50 + 1 / 205), and use this number to divide the voltage squared in order to get the power, but this is not correct. I don't know what I'm missing here. Any help will be appreciated.