One lightbulb is marked \"20 W 120 V,\" and another \"106 W 120 V\"; this means

Question

One lightbulb is marked "20 W 120 V," and another "106 W 120 V"; this means that each converts its respective power when plugged into a constant 120 V potential difference. Find the resistance of each bulb. How long does it take for 1.00 C to pass through the dim bulb? How is this charge different upon its exit from, versus its entry into, the bulb? When the charge emerges from the bulb, it has How long does it take for 1.00 J to pass through the dim bulb? How is this energy different upon its exit from, versus its entry into, the bulb? Electric potential energy is Find the cost of running the dim bulb continuously for 34.0 days if the electric company sells its product at $0.0700 per kWh. What physical quantity does the electric company sell? The electric company sells What is its price for one SI unit of this quantity?

Explanation / Answer

(a) Power rating of a bulb = P = V*V/R So, R20 = 120*120/20 = 720 R106 = 120*120/106 = 135.85 (b) The bulb with lower power rating is the dimmer one. P = I*V => I = P/V = 20/120 = 0.167 A = 0.167 C/s So, time taken for 1C charge to pass = 1/0.167 s = 6 seconds When the charge leaves the bulb it has not changed in anyway. It is the electric potential energy of the charge that hasdecreased. (c) Power rating of the bulb = 20 W = 20 J/s So, time taken for 1 J to pass through = 1/20 = 0.05 seconds Electric potential energy has been partly converted into heat andlight in the bulb. So, electric potential energy has decreased in magnitude. (d) Total energy consumed = P*t Here, P = 20W t = 34 days = 34*24 hours So, energy consumed = 20*34*24 Wh = 16.32 kWh Cost = $0.070*16.32 = $1.1424 The electric company sells electrical energy since : kWh = kilowatt hour = 1 kW * 1hr = 1000 W *3600 s =3.6*106 J which is the unit of energy. Price per J = $0.0700/(3.6*106) =$1.944*10-8/J

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