A string of 24 identical Christmas tree lights are connected in series to a 120

Question

A string of 24 identical Christmas tree lights
are connected in series to a 120 V source. The
string dissipates 59 W.
What is the equivalent resistance of the
light string?
Answer in units of ?.
003 (part 2 of 5) 10.0 points
What is the resistance of a single light?
Answer in units of ?.
004 (part 3 of 5) 10.0 points
How much power is dissipated in a single
light?
Answer in units of W.
005 (part 4 of 5) 10.0 points
One of the bulbs quits burning. The string
has a wire that shorts out the bulb ?lament
when it quits burning, dropping the resistance
of that bulb to zero. All the rest of the bulbs
remain burning.
What is the resistance of the light string
now?
Answer in units of ?.
006 (part 5 of 5) 10.0 points
How much power is dissipated by the string
now?
Answer in units of W

Explanation / Answer

Data: No. of lights, n = 24 Voltage, V = 120 V Power dissipated by the string, P = 59 W Solution: (a) Equivalent resistance, Req = V^2 / P                                         = 120^2 / 59                                         = 244.1 Ans: Equivalent resistance, Req = 244.1 (b) Resistance of single light, R = Req / n [ since they are in series ]                                           = 244.1 / 24                                           = 10.2 Ans: Resistance of single light, R = 10.2 (c) Voltage across each light, V' = V / n                                             = 120 / 24                                             = 5 V Power dissipated in single light, P' = V'^2 / R                                                     = 5^2 / 10.2                                                     = 2.45 W (or) Power dissipated in single light, P' = P / n                                                     = 59 / 24                                                     = 2.45 W Ans: Power dissipated in single light, P' = 2.45 W (d) New resistance of the light string, R' = Req - R                                                         = 244.1 - 10.2                                                         = 233.9 Ans: New resistance of the string, R' = 233.9 (e) Power dissipated by the string, P'' = V^2 / R'                                                     = 120^2 / 233.9                                                     = 61.56 W Ans: Power dissipated by the string, P'' = 61.56 W

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