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A charge of \(4.00{\rm{ }}C\) charge passes through a pocket calculator’s solar cells in \(4.00{\rm{ }}h\). What is the power output, given the calculator’s voltage output is \(3.00{\rm{ }}V\)? (See Figure \(20.40\).)

Short Answer

Expert verified

The power output of the calculator is obtained as: \(P{\rm{ }} = {\rm{ }}0.833{\rm{ }}mW\).

Step by step solution

01

Define Resistance

In an electrical circuit, resistance is a measure of the resistance to current flow. The Greek letter omega \({\rm{(\Omega )}}\) is used to represent resistance in ohms.

02

Concepts and Principles

Electric current is the magnitude of the physical quantity of electric current \({\rm{I}}\) in a wire which equals the magnitude of the electric charge \(q\) that passes through a cross-section of the wire divided by the time interval \(\Delta t\) needed for that charge to pass:

\(I{\rm{ }} = {\rm{ }}\frac{{|q|}}{{\Delta t}}\)……………..(I)

The unit of current is the ampere\(A\), which is equivalent to one coulomb per second\((C/s)\).A current of\(1A\)(one ampere, or amp) means that\(1{\rm{ }}C\)of charge passes through a cross-section of the wire every second. The direction of the current is from higher to lower potential. So, it is in the direction that positive charges that would move.

If a potential difference \(\Delta V\) is maintained across a circuit element, the power, or the rate at which energy is supplied to the element, is:\(P{\rm{ }} = {\rm{ }}I\Delta V\)………….(II)

03

The given data and the required data

  • Charge passing through the calculator is: \(q{\rm{ }} = {\rm{ }}4.00{\rm{ }}C\).
  • The time interval needed for that charge to pass is:\(\begin{aligned}{}\Delta t{\rm{ }} &= {\rm{ }}(4.00{\rm{ }}h)(\frac{{3600{\rm{ }}s}}{{1{\rm{ }}h}})\\ &= {\rm{}}14400{\rm{}}s\end{aligned}\)
  • The voltage output of the calculator is: \(\Delta V{\rm{ }} = {\rm{ }}3.00{\rm{ }}V\).
04

Evaluating the power output of the calculator

Current in the calculator is found by using Ohm's law with the help of the first equation as:

\(I{\rm{ }} = {\rm{ }}\frac{q}{{\Delta t}}\)

Entering values and we obtain:

\(\begin{aligned}{}I{\rm{ }} &= {\rm{ }}\frac{{4.00{\rm{ }}C}}{{14400{\rm{ }}s}}\\ &= {\rm{ }}\frac{1}{{3600}}A\end{aligned}\)

The power output of the calculator is found with the help of the second equation as:

\(P{\rm{ }} = {\rm{ }}I\Delta V\)

Substitute numerical values, and we get:

\(\begin{aligned}{}P{\rm{ }} &= {\rm{ }}(\frac{1}{{3600}}A)(3.00{\rm{ }}V)\\ &= {\rm{ }}8.33{\rm{ }} \times {\rm{ }}{10^{ - 4}}{\rm{ }}W\\ &= {\rm{ }}(8.33{\rm{ }} \times {\rm{ }}{10^{ - 4}}{\rm{ }}W)(\frac{{1000{\rm{ }}mW}}{{1{\rm{ }}W}})\\ &= {\rm{ }}0.833{\rm{ }}mW\end{aligned}\)

Therefore, the power output is: \(P{\rm{ }} = {\rm{ }}0.833{\rm{ }}mW\).

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Most popular questions from this chapter

Foolishly trying to fish a burning piece of bread from a toaster with a metal butter knife, a man comes into contact with \({\bf{120 V AC}}\). He does not even feel it since, luckily, he is wearing rubber-soled shoes. What is the minimum resistance of the path the current follows through the person?

Consider a person working in an environment where electric currents mightpass through her body. Construct a problem in which you calculate the resistance of insulation needed to protect the person from harm. Among the things to be considered are the voltage to which the person might be exposed, likely body resistance (dry, wet, …), and acceptable currents (safe but sensed, safe and unfelt, …).

Two different electrical devices have the same power consumption, but one is meant to be operated on \(120 - V\) AC and the other on \(240 - V\)AC.

(a) What is the ratio of their resistances?

(b) What is the ratio of their currents?

(c) Assuming its resistance is unaffected, by what factor will the power increase if a \(120 - V\) AC device is connected to \(240 - V\) AC?

How many volts are supplied to operate an indicator light on a DVD player that has a resistance of \({\bf{140}}\;{\bf{\Omega }}\), given that \({\bf{25}}{\bf{.0}}\;{\bf{mA}}\) passes through it?

Find the current through a person and identify the likely effect on her if she touches a \({\rm{120 - V AC}}\)source: (a) if she is standing on a rubber mat and offers a total resistance of \({\rm{300k\Omega ;}}\) (b) if she is standing barefoot on wet grass and has a resistance of only \({\rm{4000k\Omega }}{\rm{.}}\)

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