Light Bulbs in Series and in Parallel. Two light bulbs have constant resistances of 400Ω and 800Ω. The two light bulbs are now connected in parallel across the 120-V line. Find (d) the current through each bulb.

Verified step by step guidance

1. Identify the resistances of the two bulbs. The first bulb has a resistance of 400\(\Omega\) and the second bulb has a resistance of 800\(\Omega\).
2. Since the bulbs are connected in parallel, use the formula for the total resistance in a parallel circuit: \(\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2}\).
3. Calculate the total resistance of the circuit using the resistances of the two bulbs.
4. Use Ohm's Law, \(V = IR\), to find the total current flowing from the power source. Here, \(V\) is the voltage of the power source (120 V) and \(R\) is the total resistance calculated in the previous step.
5. Determine the current through each bulb using Ohm's Law again, \(I = \frac{V}{R}\), where \(V\) is the voltage across each bulb (120 V, since they are in parallel) and \(R\) is 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. This relationship is expressed mathematically as V = I * R. Understanding this law is essential for calculating the current through each light bulb when connected in parallel.

Resistors in Parallel

When resistors are connected in parallel, the total or equivalent resistance (R_eq) can be calculated using the formula 1/R_eq = 1/R1 + 1/R2. In this case, the voltage across each resistor remains the same, which is equal to the source voltage. This concept is crucial for determining how the current divides among the light bulbs based on their individual resistances.

Current Division

Current division refers to the way current is distributed among parallel branches in a circuit. The current through each branch is inversely proportional to its resistance. For two resistors in parallel, the current through each can be calculated using the formula I_x = (V/R_x) for each resistor, where V is the voltage across the parallel combination. This principle is key to finding the current through each light bulb in the given problem.