Question

Consider the classic problem with holiday lights, one little bulb goes out and the whole string goes out. First consider a string of 50 lights in series that plugs into a standard 120VAC outlet and consumes 40 Watts of power.
a. What is the current flowing through each bulb?
b. What is the voltage drop across each bulb?
c. If when a lightbulb burns out the resistance of the bulb becomes infinite, what is the current flowing through that bulb? What is the current flowing through the entire circuit?
d. If a bulb breaks open, exposing the two wires inside and they touch together (i.e., on) what would be the current flowing through this "short circuit"?
e. If the bulbs were instead wired in parallel and a bulb broke open and shorted, what would be the current flowing this short circuit?
f. Which configuration is safer, series or parallel? Why?

Answer 1

Answer:

a. 0.33 Amp

b. 2.4 Volt

c. 0

d. 2.45 Amp

e. Infinite

f. Series is safer

Explanation:

Series Connection of Resistors

When two or more resistors are connected in series, the current through each one of them is the same, and the voltage divides depending on the particular value of each resistance. If all the resistances are equal, then the voltage is equally divided.

a. The string of 50 bulbs is connected to a 120 VAC outlet and consumes 40 W. The power of a circuit is given by

$P=V.I$

Solving for I

$\displaystyle I=\frac{P}{V}=\frac{40}{120}=0.33\ Amp$

Since all the bulbs are connected in series the current is the same for all of them.

b. The voltage is equally divided, so each bulb has  120/50= 2.4 V

c. If one of the bulbs burns out and its resistance becomes infinite, then the series circuit is open and no current flows through it, neither through the rest of the bulbs. The typical case of the whole string going out.

d. If one of the bulbs short circuits, the resistance of that bulb is zero and the voltage is distributed by the 49 remaining bulbs. Thus the new current is

$\displaystyle I=\frac{V}{R}=\frac{120}{49}=2.45\ A$

e. If the bulbs were connected in parallel, all of them would have the same voltage, and the total current will be equally divided among them. In that case, a short circuit in one of the bulbs will cause a parallel short, theoretically producing an infinite current and making the short circuit protection blow up.

f. The condition described above makes the strings be made of series-connected bulbs which is safer than the parallel circuit. If a single bulb shorts, the entire string goes out in a series connection, but the breaker would trigger disconnection of the house circuit if it's a parallel connection. That is why we must deal with unusable strings instead of burning cables.