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Chapter 27: Problem 13

A lightbulb has a resistance of \(240 \Omega\) when operating with a potential difference of \(120 \mathrm{V}\) across it. What is the current in the lightbulb?

Short Answer

Expert verified
The current flowing through the lightbulb is \(0.5\) amperes.

Step by step solution

01

Identification of Known Parameters

In this case, the resistance of the lightbulb \( R \) is given as \(240 \Omega\), and the potential difference or voltage \( V \) across the lightbulb is \( 120 \) volts.
02

Application of Ohm's Law

Ohm's law is defined as \( V = I \times R \), which can be rearranged to solve for current: \( I = \frac{V}{R} \). Plug the known values into the equation: \( I = \frac{120 \mathrm{V}}{240 \Omega} \).
03

Calculation

Perform the division on the right hand side of the equation to get the current value: \( I = 0.5 \) amperes.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Electrical Resistance
Electrical resistance is a measure of how much an object opposes the flow of electric current. Imagine it like a bumpy road that makes it harder for a car to speed through.
Just like rough roads slow down vehicles, high resistance slows down electric flow.
  • Resistance (\( R \)) is measured in ohms (\( \Omega \)).
  • A higher resistance means that it's harder for electricity to flow.
  • Materials like copper have low resistance and are good conductors of electricity.
In the case of our lightbulb, the resistance is \( 240 \Omega \). This value tells us how much the bulb resists the flow of current. Engineers choose specific resistance values to ensure devices like lightbulbs operate safely and effectively.
Electric Current
Electric current is the flow of electric charge. It's the movement of electrons through a conductor, like water flowing through a pipe.
Current is measured in amperes (A), which tells us how much charge is flowing per second.
  • Current (\( I \)) flows from higher to lower potential energy.
  • One ampere equals the flow of one coulomb of charge per second.
  • Current can flow in one direction (DC) or alternate directions (AC).
In our lightbulb problem, the current flow was calculated as \( 0.5 \) amperes.This means half of a coulomb of charge is flowing through the bulb every second. The right amount of current ensures that the lightbulb shines brightly and doesn't blow up.
Potential Difference
Potential difference, also known as voltage, is the work required to move a unit charge from one point to another.
It can be thought of as the pressure pushing the current through a circuit.
  • Measured in volts (V).
  • A higher voltage means more "pressure" is driving the charge through the circuit.
  • It is the potential energy difference per unit charge.
In the lightbulb, the potential difference is \( 120 \) volts.This voltage sets up the conditions for current to flow, powering the bulb to emit light. Providing the correct potential difference ensures that electronic devices operate as intended.

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Most popular questions from this chapter

One rechargeable battery of mass \(15.0 \mathrm{g}\) delivers to a CD player an average current of \(18.0 \mathrm{mA}\) at \(1.60 \mathrm{V}\) for \(2.40 \mathrm{h}\) before the battery needs to be recharged. The recharger maintains a potential difference of \(2.30 \mathrm{V}\) across the battery and delivers a charging current of \(13.5 \mathrm{mA}\) for \(4.20 \mathrm{h}\) (a) What is the efficiency of the battery as an energy storage device? (b) How much internal energy is produced in the battery during one charge-discharge cycle? (b) If the battery is surrounded by ideal thermal insulation and has an overall effective specific heat of \(975 \mathrm{J} / \mathrm{kg}^{\circ} \mathrm{C},\) by how much will its temperature increase during the cycle?

Make an order-of-magnitude estimate of the cost of one person's routine use of a hair dryer for 1 yr. If you do not use a blow dryer yourself, observe or interview someone who does. State the quantities you estimate and their values.

A toaster is rated at \(600 \mathrm{W}\) when connected to a \(120-\mathrm{V}\) source. What current does the toaster carry, and what is its resistance?

A current density of \(6.00 \times 10^{-13} \mathrm{A} / \mathrm{m}^{2}\) exists in the atmosphere at a location where the electric field is \(100 \mathrm{V} / \mathrm{m}\) Calculate the electrical conductivity of the Earth's atmosphere in this region.

The current in a resistor decreases by 3.00 A when the voltage applied across the resistor decreases from \(12.0 \mathrm{V}\) to \(6.00 \mathrm{V} .\) Find the resistance of the resistor.
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