A string of 29 identical Christmas tree lights

are connected in series to a 120 V source. The
string dissipates 65 W.
What is the equivalent resistance of the
light string?
Answer in units of Ω

Power = 65 W = V^2/R

V = 120 V

where R is the resistance of the string. Solve for it

The number of lights is not needed.

205.7142857 ohms

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 voltage (V) across a resistor is equal to the current (I) flowing through it multiplied by its resistance (R): V = I * R

The formula for power dissipation is given by: P = V^2 / R, where P is the power dissipated, V is the voltage across the resistor, and R is the resistance.

Given that the voltage across the light string is 120V and the power dissipated is 65W, we can rearrange the power dissipation formula to solve for the resistance:

R = V^2 / P

Plugging in the values, we have:
R = (120V)^2 / 65W

Calculating this equation gives us:
R = 14400V^2 / 65W

Simplifying further, we get:
R ≈ 221.538 Ω

Therefore, the equivalent resistance of the light string is approximately 221.538 Ω.

To find the equivalent resistance of the light string, we can use Ohm's Law. Ohm's Law states that the current flowing through a circuit is directly proportional to the voltage applied across it and inversely proportional to the resistance.

First, we need to find the current flowing through the circuit. We can use the formula:
Power (P) = Voltage (V) * Current (I)

Rearranging the formula to solve for current, we get:
Current (I) = Power (P) / Voltage (V)

Substituting the given values, we have:
Current (I) = 65 W / 120 V

Now, using Ohm's Law, we can find the equivalent resistance of the light string:
Resistance (R) = Voltage (V) / Current (I)

Substituting the calculated values, we get:
Resistance (R) = 120 V / (65 W / 120 V)

Simplifying the equation, we get:
Resistance (R) = 120 V^2 / 65 W

Calculating this expression, the equivalent resistance of the light string is approximately 220.615 Ω.