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 first need to find the current passing through the string.
We know that the power dissipated by the string is 63 W, and the voltage across the string is 120 V. We can use the formula for power, P = VI, where P is the power, V is the voltage, and I is the current.
So, we can rearrange the formula to solve for current:
I = P / V
Plugging in the values, we get:
I = 63 W / 120 V
Calculating this, we find that the current passing through the string is 0.525 A.
Now, since the lights are connected in series, the current passing through each light is the same. So, the current passing through each light is also 0.525 A.
We can use Ohm's Law to find the resistance of each light. Ohm's Law states that resistance (R) is equal to voltage (V) divided by current (I):
R = V / I
Plugging in the values, we get:
R = 120 V / 0.525 A
Calculating this, we find that the resistance of each light is approximately 228.57 Ω.
Since we have 26 lights in the string, the equivalent resistance of the light string can be found by summing up the resistances of each light:
Equivalent Resistance = 26 * Resistance of each light
Equivalent Resistance = 26 * 228.57 Ω
Calculating this, we find that the equivalent resistance of the light string is approximately 5943.82 Ω.