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) = Ω R(75 W 120 V) = Ω (b) During what time interval does 2.30 C pass into lightbulb A? Δt = s (d) In what time interval does 3.00 J enter lightbulb A? Δt = 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. $

Answer 1

(a)   For the resistance of lightbulb A,

P_A  = (V_A)^2 / R_A

=> R_A  = (V_A)^2 / P_A  = (120)^2 / 40 = 360 Ω

(b)   For the resistance of lightbulb B,

P_B  = (V_B)^2 / R_B

=>   R_B  = (V_B)^2 / P_B  = (120)^2 / 75 = 192 Ω

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

Q_A  = (I_A)*t

=>   t = Q_A / I_A

= Q_A / (V_A / R_A) = 2.3 / (120 / 360) = 6.9 s

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

E_A = P_A*t

        =>   t  = E_A / P_A = 3 / 40 = 0.075 s

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

Power of lightbulb A: P_A = 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)*(P_A*t) = ($ 0.11)*(0.04*480) = $ 2.112