Some light-dimmer switches use a variable resistor as shown in the figure. The s

Question

Some light-dimmer switches use a variable resistor as shown in the 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 Rvar = 150? at x = 1).

1)What is the power expended in the lightbulb if x = 1.00.

the answer is 60 W

2)What is the power expended in the lightbulb if x = 0.61?????

What is the power expended in the lightbulb if x = 0.35???????

Some light-dimmer switches use a variable resistor as shown in the 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 Rvar = 150 at x = 1). 1)What is the power expended in the lightbulb if x = 1.00. the answer is 60 W 2)What is the power expended in the lightbulb if x = 0.61????? What is the power expended in the lightbulb if x = 0.35???????

Explanation / Answer

Power when x = 1

V2/R = 1202/240 = 60 W (ans)

X= 0.61

Resistance parallel to bulb = 0.61*150 = 91.5

Net resistance of the circuit = 58.5 + 91.5*240/(91.5+240) = 124.74 ohm

current in the circuit = 120/124.74 = 0.96196 A

voltage drop across 58.5 ohm = 58.5*0.96196 = 56.27 V

Power across the bulb = (120-56.27)2/240 = 16.92 W (ans)

x = 0.35

Net resistance = 97.5 + 52.5*240/(52.5+240) = 140.576 ohm

voltage drop across 97.5 = 97.5*(120/140.576) = 83.228 V

Power across the bulb = (120-83.228)2/240 = 5.6339 W (ans)

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