Question

How many coulombs are provided by a current of \(0.010 \mathrm{~mA}\) in the calculator battery that can operate for 1000 hours? (a) \(1.0\) (b) 10 (c) \(0.010\) (d) 36

Short answer

36

Step-by-step solution

Convert current to amperes

First, convert the current from milliamperes to amperes. Since there are 1000 milliamperes in an ampere, you would divide the current by 1000. So, if you have 0.010 milliamperes, in amperes it would be \(0.010 \mathrm{~mA} = 0.010 \times 10^{-3} \mathrm{~A}\).

Convert time to seconds

Convert the time from hours to seconds because the charge in coulombs is calculated based on time in seconds. As there are 3600 seconds in an hour, multiply the time in hours by 3600. Therefore, \(1000 \mathrm{~hours} = 1000 \times 3600 \mathrm{~seconds}\).

Calculate the total charge in coulombs

Use the formula \(Q = I \times t\) where \(Q\) is the charge in coulombs, \(I\) is the current in amperes, and \(t\) is the time in seconds. Plugging the values into the formula gives \(Q = 0.010 \times 10^{-3} \mathrm{~A} \times 1000 \times 3600 \mathrm{~s}\). Calculating this result yields \(Q = 0.010 \times 10^{-3} \times 3600000\) coulombs.

Key concepts

Electric Current

Understanding the flow of electric charge is crucial, and this flow is referred to as electric current. Imagine it as water flowing through a pipe; similarly, electric current is the flow of electrons through a conductor. The unit used to measure this flow is the ampere (A), which represents one coulomb of charge passing through a point in a circuit per second.

When talking about smaller currents, we often use the unit milliamperes (mA), where 1 mA equals 0.001 A. So, if a current of 0.010 mA is stated, it's a very small current, enough to power something like a calculator, which doesn't require much energy to operate. Such small currents are important for battery-operated devices as they allow the battery to last for extended periods, like the 1000 hours mentioned in our problem.

Coulomb's Law

While our exercise doesn't directly involve Coulomb's Law, it's worth noting that the concept of charge calculation stems from this fundamental law in electrostatics. Coulomb's Law describes the force between two charged particles: like charges repulse each other, and unlike charges attract. This law helps us understand that charges are at the core of electric phenomena. The quantity of charge is measured in coulombs (C), and your calculator battery, for instance, generates a stream of charge that we measure in coulombs to determine how long it will last.

Unit Conversion

Unit conversions are essential in physics numerical problems to ensure consistency in the measurements. In our case, we deal with two conversions: from milliamperes to amperes and from hours to seconds. This is because the standard unit for electric current in the International System of Units (SI) is amperes, and the standard unit for time is seconds. By converting 0.010 mA to 0.00001 A, and 1000 hours to 3,600,000 seconds, we set up our calculation using consistent SI units, enabling a straightforward computation of the total charge.

Physics Numerical Problems

Working through physics numerical problems often involves applying formulas, as we did with the charge calculation formula. These exercises reinforce the understanding of physical concepts and manipulate units correctly. A clear step-by-step approach like the one used in the solution helps break down complex problems into manageable parts:

• First, identify the known quantities and their units.
• Convert to the necessary SI units if needed.
• Apply the appropriate physical formula.
• Carry out the numerical calculation carefully.

For our original problem, using the charge calculation formula, alongside the correct conversions, we calculated the number of coulombs generated by the battery, which is essential for determining the device's operational lifespan.