A string of 15 identical Christmas tree lights are connected in series to a 127 V source. The string dissipates 58 W.What is the equivalent resistance of the light string?
Answer in units of Ω
See previous post.
To find the equivalent resistance of the light string, we can use Ohm's Law and the formula for power dissipation.
Ohm's Law states that the current (I) flowing through a circuit is equal to the voltage (V) divided by the resistance (R):
I = V / R
The formula for power dissipation is given by:
P = V * I
Given that the voltage (V) is 127 V and the power dissipation (P) is 58 W, we can rearrange the formula for power dissipation to solve for current (I):
I = P / V
Substituting the given values, we have:
I = 58 W / 127 V
Simplifying this expression, we find that the current flowing through the circuit is approximately 0.457 A.
Since the Christmas tree lights are connected in series, the same current flows through each light bulb. Therefore, the equivalent resistance (Req) of the light string can be calculated using Ohm's Law:
Req = V / I
Substituting the known values, we have:
Req = 127 V / 0.457 A
Calculating this expression, we find that the equivalent resistance of the light string is approximately 277.9 Ω.