Question

A \(100 .-W, 240,-V\) European light bulb is used in an American household, where the electricity is delivered at \(120 . \mathrm{V}\). What power will it consume?

Short answer

Answer: 25W

Step-by-step solution

Determine the resistance of the light bulb

Before calculating the power consumption, we first need to determine the resistance of the light bulb. To do this, we can use Ohm's Law, which states that voltage equals current multiplied by resistance: \(V=IR\). We can rewrite this formula as \(R=V/I\). We don't have the current (I) yet, so let's use the formula for power: \(P=IV\), and rewrite it as \(I=P/V\). Now, using the given power (100W) and voltage (240V), we can find the current: \(I = 100/240 = 5/12 \ \mathrm{A}\).

Calculate the resistance of the light bulb

Now that we have the current, we can find the resistance using the formula \(R=V/I\). Plugging in the values we found: \(R = 240/(5/12)\). This simplifies to \(R=576 \ \Omega\).

Determine the power consumed in an American household

The power formula is \(P=IV\). We have the resistance, so let's find the current consumption in the American household with 120V using Ohm's Law: \(I=V/R\). Now we have: \(I=120 / 576 = 5/24\ \mathrm{A}\).

Calculate the power consumption

We now have both the voltage and current. We can use the power equation, \(P=IV\), to find the power consumed by the light bulb in the American household: \(P=(5/24) \cdot 120\). This results in the power consumption being \(P=25 \ \mathrm{W}\).