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 (c) the total power dissipated in both bulbs.

Verified step by step guidance

1. Calculate the total resistance of the bulbs when connected in series. The total resistance, R_{total}, is the sum of the individual resistances: R_{total} = R_1 + R_2.
2. Use Ohm's Law to find the total current flowing through the circuit when the bulbs are connected in series. Ohm's Law is given by I = V / R, where V is the voltage across the circuit and R is the total resistance.
3. Calculate the power dissipated by each bulb using the formula P = I^2 \times R, where P is the power, I is the current calculated in step 2, and R is the resistance of each bulb.
4. Add the power dissipated by each bulb to find the total power dissipated in the circuit. The total power, P_{total}, is given by P_{total} = P_1 + P_2, where P_1 and P_2 are the powers dissipated by the first and second bulb, respectively.
5. The total power dissipated in both bulbs when connected in series across a 120-V line is the sum obtained in step 4.

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 as V = IR, which is fundamental for analyzing electrical circuits, including those with resistors in series or parallel.

Power in Electrical Circuits

The power (P) dissipated in an electrical circuit is calculated using the formula P = IV, where I is the current and V is the voltage. In the context of resistors, power can also be expressed as P = I²R or P = V²/R, depending on the known quantities. Understanding how to calculate power is essential for determining the total power dissipated in light bulbs connected in series.

Series and Parallel Circuits

In a series circuit, components are connected end-to-end, so the same current flows through each component, and the total resistance is the sum of individual resistances. In contrast, in a parallel circuit, components are connected across the same voltage source, resulting in different currents through each component. Knowing how to analyze these configurations is crucial for solving problems related to total resistance and power dissipation.