Light Bulbs in Series and in Parallel. Two light bulbs have constant resistances of 400Ω and 800Ω. If the two light bulbs are connected in series across a 120-V line, find (a) the current through each bulb.

Verified step by step guidance

1. Step 1: Calculate the total resistance of the bulbs when connected in series. The total resistance, R_total, is the sum of the individual resistances. Use the formula: R_total = R1 + R2, where R1 and R2 are the resistances of the two bulbs.
2. Step 2: Use Ohm's Law to find the current flowing through the circuit. Ohm's Law is given by V = IR, where V is the voltage across the circuit, I is the current through the circuit, and R is the resistance of the circuit. Rearrange the formula to solve for I: I = V / R_total.
3. Step 3: Substitute the values from Step 1 into the formula from Step 2 to calculate the current. Use the total resistance you calculated and the given voltage of the circuit.
4. Step 4: Since the bulbs are connected in series, the current flowing through each bulb is the same. The current you calculated in Step 3 is the current through each bulb.
5. Step 5: Verify your calculations by checking the units and ensuring that the values make sense physically. The current should be in amperes (A).

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. This relationship is expressed mathematically as V = I * R. Understanding this law is essential for calculating the current in electrical circuits, especially when dealing with resistances in series or parallel.

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. For the given light bulbs, the total resistance can be calculated by adding the resistances of the two bulbs, which affects the overall current drawn from the voltage source.

Total Resistance Calculation

To find the total resistance in a series circuit, you simply add the resistances of all components. For two resistors, R_total = R1 + R2. In this case, with resistances of 400Ω and 800Ω, the total resistance is 1200Ω. This total resistance is crucial for determining the current flowing through the circuit when connected to a voltage source.