Neglect the internal resistance of a battery unless the problem refers to it. Ten 7.0-W Christmas tree lights are connected in series to each other and to a 120-V source. What is the resistance of each bulb?

Verified step by step guidance

1. Determine the total power of the Christmas tree lights. Since there are 10 bulbs, each rated at 7.0 W, the total power is given by: $P=10\times 7.0 W$.
2. Use the formula for power in terms of voltage and resistance for the entire circuit: $P=\frac{V^2}{R}$, where $V$ is the total voltage (120 V) and $R$ is the total resistance of the circuit.
3. Rearrange the formula to solve for the total resistance: $R=\frac{V^2}{P}$. Substitute the values for $V=120$ and $P=70$ W (calculated in step 1).
4. Since the bulbs are connected in series, the total resistance is the sum of the individual resistances. Let $R$_i represent the resistance of each bulb. Then, $R=10\times R$_i. Rearrange to solve for $R$_i: $R$_i=R10.
5. Substitute the total resistance value (calculated in step 3) into the equation from step 4 to find the resistance of each bulb.

Key Concepts

Ohm's Law

Ohm's Law states that the current (I) flowing through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R) of the conductor. It is mathematically expressed as V = I * R. This fundamental principle is essential for analyzing electrical circuits and calculating resistance, current, and voltage.

Power in Electrical Circuits

The power (P) consumed by an electrical device is defined as the rate at which it converts electrical energy into another form of energy, such as light or heat. It is calculated using the formula P = V * I, where V is voltage and I is current. In this problem, the power rating of the Christmas tree lights helps determine the total power consumed and, subsequently, the resistance of each bulb.

Series Circuits

In a series circuit, components are connected end-to-end, so the same current flows through each component. The total resistance in a series circuit is the sum of the individual resistances. This concept is crucial for understanding how the voltage from the source is distributed across the connected bulbs, allowing for the calculation of the resistance of each bulb based on the total voltage and power consumed.