A string of 26 identical Christmas tree lights
are connected in series to a 120 V source. The
string dissipates 63 W.
What is the equivalent resistance of the
light string?
Answer in units of Ω.
To find the equivalent resistance of the light string, we can use Ohm's Law and the formula for power dissipation.
First, let's recall Ohm's Law:
V = I * R
Where:
V is the voltage across the circuit (120 V in this case),
I is the current flowing through the circuit, and
R is the resistance of the circuit.
The formula for power dissipation is:
P = V * I
Where:
P is the power dissipated by the circuit (63 W in this case),
V is the voltage across the circuit, and
I is the current flowing through the circuit.
We can rearrange the formula for power dissipation to solve for current:
I = P / V
Substituting the given values, we have:
I = 63 W / 120 V
I ≈ 0.525 A
Now, using Ohm's Law, we can rearrange the formula to solve for resistance:
R = V / I
Substituting the given values, we have:
R = 120 V / 0.525 A
R ≈ 228.57 Ω
Therefore, the equivalent resistance of the light string is approximately 228.57 Ω.