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Electric power is volts times amperes \((P=V i)\). When a car battery at \(12 \mathrm{~V}\) is charged with 6 amps for \(3 \mathrm{~h}\), how much energy is delivered?

Short Answer

Expert verified
216 Wh of energy is delivered.

Step by step solution

01

Understand the Formula

The formula for electric power is given by \( P = V \, i \), where \( P \) is the power in watts, \( V \) is the voltage in volts, and \( i \) is the current in amperes.
02

Calculate Power

To find the power, multiply the voltage \( V = 12 \, \mathrm{V} \) by the current \( i = 6 \, \mathrm{A} \). \[ P = 12 \, \mathrm{V} \times 6 \, \mathrm{A} = 72 \, \mathrm{W} \]
03

Convert Time to Hours

The problem states that the car battery is charged for \( 3 \, \mathrm{hours} \), so no conversion is needed as the time is already in hours.
04

Calculate Energy Delivered

Energy delivered can be calculated by multiplying the power by the time the current is applied. The energy \( E \) in watt-hours is given by:\[ E = P \times t = 72 \, \mathrm{W} \times 3 \, \mathrm{h} = 216 \, \mathrm{Wh} \]

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Key Concepts

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

Voltage
Voltage, often referred to as electric potential or electromotive force, is a critical component in electric circuits. It represents the potential difference or the pushing force that drives electric charges through a conductor. In simpler terms, think of voltage as the pressure of electricity flowing in our circuits. The unit of voltage is volts (V). High voltage means more electrical pressure, which can push more current through the system.
In our example, the car battery has a voltage of 12 V. This means that it provides a driving force that allows the electric current to pass through the circuit. Understanding voltage is essential because it directly affects how much power the battery can deliver to a device. Without sufficient voltage, even if a battery has ample current capacity, it cannot perform effectively.
Voltage is to a circuit what water pressure is to a hose: it pushes the electrons, akin to pushing water, through the electrical pathway. Knowing how voltage influences the overall energy transmission within a system aids you in predicting how devices will perform when connected to different power sources.
Current
Current is the rate at which electric charges flow through a conductor. It's measured in amperes, abbreviated as amps (A). One ampere corresponds to approximately 6.242 x 10^18 electrons moving through a point in the circuit each second. This flow of electrons is what creates electric power.
The current flows from a point of higher electrical potential (voltage) to a point of lower potential. In the exercise, the car battery provides a current of 6 A. This value tells us how many charges are flowing, essentially indicating the number of electrons moving past a certain point per second.
- **Steady Current**: In a DC (Direct Current) circuit like the car battery example, the current flows in a single direction, uninterrupted. - **Relationship With Voltage**: Current depends on voltage; higher voltage usually means higher current is possible, assuming the resistance stays constant.
Understanding current is vital to controlling electric circuits. It allows for determining how much energy can be harnessed over time to power devices successfully.
Energy Conversion
Energy conversion in electrical systems refers to transforming energy from one form to another. When dealing with batteries or power systems, it is crucial to understand how energy is consumed, stored, and converted into usable power.
In our specific problem, the charged car battery converts electrical energy into chemical energy when it is being charged. This stored energy can later be converted back into electrical energy as the car operates. Energy conversion in the form of electricity is computed using the formula: \[ E = P \times t \]where \( E \) is the energy in watt-hours (Wh), \( P \) is power in watts (W), and \( t \) is time in hours (h).
- **Battery Storage**: During charging, a 12 V battery at 6 amps over 3 hours, as in this scenario, stores energy efficiently. - **Practical Conversion**: In these calculations, the energy delivered to the battery is 216 Wh. This highlights how much useful work can be derived once this stored energy is converted back to its original form.
Energy conversion allows for significant flexibility in how energy is used and transferred. As you tackle similar problems, remember the interplay between power, time, and energy, ensuring maximum efficiency in energy conversion.

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