Eight holiday lights are connected in series as shown in
Fig. 5.83.
a. If the set is connected to a 120-V source, what is the
current through the bulbs if each bulb has an internal
resistance of 28�
1
8
� �?
b. Determine the power delivered to each bulb.
c. Calculate the voltage drop across each bulb.
d. If one bulb burns out (that is, the filament opens),
what is the effect on the remaining bulbs
To calculate the current through the bulbs, we need to use Ohm's Law, which states that the current (I) flowing through a circuit is equal to the voltage (V) divided by the resistance (R). In this case, the resistance of each bulb is given as 28/8 Ω.
a. To find the total resistance of the circuit, we need to add up the resistances of all the bulbs in series. Since there are 8 bulbs, the total resistance (R_total) is 8 * (28/8) Ω = 28 Ω.
Next, we can use Ohm's Law to find the current. The voltage (V) is given as 120 V.
I = V / R_total = 120 V / 28 Ω ≈ 4.29 A
Therefore, the current through the bulbs is approximately 4.29 A.
b. To determine the power delivered to each bulb, we can use the formula P = VI, where P is the power, V is the voltage, and I is the current.
For each bulb, the voltage is the same as the voltage drop across each bulb (which we will calculate in part c) and the current is the same as the current calculated in part a.
P = V * I = 28/8 Ω * 4.29 A ≈ 14.79 W
Therefore, the power delivered to each bulb is approximately 14.79 W.
c. To calculate the voltage drop across each bulb, we can use Ohm's Law again.
V = I * R = 4.29 A * 28/8 Ω ≈ 14.96 V
Therefore, the voltage drop across each bulb is approximately 14.96 V.
d. If one bulb burns out and its filament opens, the circuit becomes incomplete. This increases the total resistance of the circuit, as the burned-out bulb no longer provides a conducting path.
The new total resistance would be the sum of the resistances of the remaining bulbs. If one bulb burned out, there would only be 7 working bulbs left.
New R_total = 7 * (28/8) Ω = 24.5 Ω
To find the new current, we can use Ohm's Law: I = V / R_total.
New I = 120 V / 24.5 Ω ≈ 4.90 A
The current through the remaining bulbs increases when one bulb burns out. As a result, the remaining bulbs may become brighter, and there is an increased risk of overloading and potentially burning out more bulbs. It is generally recommended to replace a burned-out bulb as soon as possible.