Problem 17 - Applied Physics

Question

Find the power output of a cell phone charger that delivers \(40 \overline{0} \mathrm{~mA}\) of current at \(5.90 \mathrm{Vdc}\).

Step-by-Step Solution

Answer

The power output of the charger is 2.36 W.

Step 1: Understand the Formula for Power

To find the power output of the charger, we need to use the formula for electrical power, which is given by \[ P = IV \]where \( P \) is power in watts, \( I \) is current in amperes, and \( V \) is voltage in volts.

Step 2: Convert Current to Amperes

The problem gives the current as \( 40 \overline{0} \mathrm{~mA} \). We need to convert this value from milliamperes to amperes. We do this by dividing by 1000:\[ I = 40\overline{0} \mathrm{~mA} = 0.40 \mathrm{~A} \].

Step 3: Insert Values into the Formula

Now that we have the correct units, substitute the values for current and voltage into the power formula:\[ P = 0.40 \mathrm{~A} \times 5.90 \mathrm{~V} \].

Step 4: Calculate the Power Output

Multiply the current and the voltage to find the power:\[ P = 0.40 \mathrm{~A} \times 5.90 \mathrm{~V} = 2.36 \mathrm{~W} \].

Key Concepts

Current Conversion

Before we can start using the power formula, it's important to ensure all measurements are in the correct units. In electrical calculations, current is generally expressed in amperes (A). However, sometimes it is given in milliamperes (mA), as in our example with a cell phone charger delivering \(400 \mathrm{~mA}\).
1 milliampere is equal to \(0.001\) amperes.

• To convert from milliamperes to amperes, you divide by 1,000.
• So, \(400\mathrm{~mA} = 400 / 1000 = 0.40 \mathrm{~A}\).

It is essential to do these conversions so that the next formula we use can work correctly. Otherwise, our calculations for power would be incorrect.

Power Formula

The power formula is a fundamental concept in electrical circuits. It's used to calculate how much energy is converted by electrical devices per unit time. The power formula can be represented as:

• \(P = IV\)
• Where \(P\) is power in watts (W), \(I\) is current in amperes (A), and \(V\) is voltage in volts (V).

This formula tells you that the electrical power is the product of the current flowing through the device and the voltage across it.
Understanding how to manipulate and substitute values into this formula is crucial for calculating power output exactly as needed.

Voltage in Electrical Circuits

Voltage is sometimes referred to as electrical potential difference. It can be thought of as the force that pushes electric charges through a circuit. Voltage is measured in volts (V) and is an essential component in determining electrical power.

If you imagine electricity flowing through a circuit like water flowing through a hose, voltage would be akin to water pressure. Hence, a higher voltage typically means a stronger current flow, assuming resistance is constant.
For our cell phone charger, voltage is given as \(5.90 \mathrm{Vdc}\) (where dc stands for direct current). This voltage value is used in the power formula to find the correct power output of whatever device you are examining.

SI Units for Electrical Measurements

SI units (International System of Units) are the standard units universally accepted in scientific communities for measuring various quantities.

In electricity, the relevant SI units include:

• Amperes (A) for current
• Volts (V) for voltage
• Watts (W) for power

Using these standard units ensures consistency and accuracy in calculations and allows for clear communication of results.
Converting measurements to their proper SI units helps prevent possible errors and misunderstandings. Therefore, it is a basic skill every student should master when dealing with electrical measurements and calculations.