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 the total power dissipated in both bulbs.

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First, understand that when resistors (or light bulbs in this case) are connected in parallel, the voltage across each resistor is the same as the source voltage. Therefore, both bulbs have 120 V across them.

Next, use Ohm's Law to find the current through each bulb. Ohm's Law is given by:

I = \frac{V}{R}

. Calculate the current through the 400Ω bulb and the 800Ω bulb separately.

Calculate the power dissipated by each bulb using the formula for electrical power:

P = V I

. Since you have already calculated the current through each bulb, multiply the voltage (120 V) by the current for each bulb to find the power dissipated by each bulb.

Add the power dissipated by the 400Ω bulb and the 800Ω bulb to find the total power dissipated in the circuit. This is because power in parallel circuits is additive.

Finally, ensure that your units are consistent and check your calculations for any errors. The total power dissipated will be the sum of the power dissipated by each bulb.

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주요 개념

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Ohm's Law

Ohm's Law states that the current through a conductor between two points is directly proportional to the voltage across the two points, and inversely proportional to the resistance. It is expressed as V = IR, where V is voltage, I is current, and R is resistance. This law is fundamental in calculating the current flowing through each bulb when connected in parallel.

Parallel Circuit

In a parallel circuit, components are connected across common points or junctions, providing multiple paths for current to flow. The voltage across each component is the same, but the total current is the sum of the currents through each component. Understanding parallel circuits is crucial for determining how the 120-V line affects each bulb individually.

Power Dissipation

Power dissipation in electrical circuits refers to the conversion of electrical energy into heat energy in resistive components. It is calculated using the formula P = VI, where P is power, V is voltage, and I is current. Alternatively, in terms of resistance, it can be expressed as P = V^2/R for each bulb. Calculating power dissipation helps determine the total energy used by both bulbs.