Lightbulb A is marked \"40 W 120 V\", and lightbulb B is marked \"75 W 120 V\".

Question

Lightbulb A is marked "40 W 120 V", and lightbulb B is marked "75 W 120 V". These labels mean that each lightbulb has its respective power delivered to it when it is connected to a constant 120-V source. (a) Find the resistance of each lightbulb. R(40 W 120 V) = R(75 W 120 V) = (b) During what time interval does 2.30 C pass into lightbulb A? t = s (d) In what time interval does 3.00 J enter lightbulb A? t = s (e) Find the cost of running lightbulb A continuously for 20.0 days, assuming the electric company sells its product at $0.110 per kWh. $

Explanation / Answer

(a)   For the resistance of lightbulb A,

PA  = (VA)^2 / RA

=> RA  = (VA)^2 / PA  = (120)^2 / 40 = 360

(b)   For the resistance of lightbulb B,

PB  = (VB)^2 / RB

=>   RB  = (VB)^2 / PB  = (120)^2 / 75 = 192

(c)   For the time interval to pass 2.30 C charge into lightbulb A,

QA  = (IA)*t

=>   t = QA / IA

= QA / (VA / RA) = 2.3 / (120 / 360) = 6.9 s

(d) For the time interval for 3.00 J of energy to enter lightbulb A,

EA = PA*t

        =>   t  = EA / PA = 3 / 40 = 0.075 s

(e)   For the cost of running lightbulb A continuously for 20.0 days,

Power of lightbulb A: PA = 40 W = 0.04 kW

The total time in 20 days: t = 20*24 hr = 480 hr

Since the given rate = $ 0.11 per kWh

=> The Total Cost = ($ 0.11)*(PA*t) = ($ 0.11)*(0.04*480) = $ 2.112

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