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Chapter 18: Problem 21

A \(12-\Omega\) resistor has a potential difference of \(16 \mathrm{V}\) across it. What current flows through the resistor?

Short Answer

Expert verified
Answer: The current flowing through the resistor is \(\frac{4}{3}\,\mathrm{A}\) or approximately \(1.33\,\mathrm{A}\).

Step by step solution

01

Write down the given values

The problem gives us the resistance (R) which is \(12\,\Omega\) and the potential difference (V) which is \(16\,V\).
02

Write down the formula for Ohm's Law

Ohm's Law is \(V = IR\). We need to solve for the current (I) in this case.
03

Rearrange the formula to solve for I

Since we are trying to find the current (I), we need to rearrange Ohm's Law to isolate I on one side. To do this, divide both sides by R. The rearranged formula is \(I = \frac{V}{R}\).
04

Plug in the given values and calculate the current

Now we can substitute the given values of V and R into the formula. \(I = \frac{16\mathrm{V}}{12\Omega} = \frac{4}{3}\,\mathrm{A}\) The current flowing through the resistor is \(\frac{4}{3}\,\mathrm{A}\) or approximately \(1.33\,\mathrm{A}\).

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Most popular questions from this chapter

A \(500-\) W electric heater unit is designed to operate with an applied potential difference of \(120 \mathrm{V}\). (a) If the local power company imposes a voltage reduction to lighten its load, dropping the voltage to $110 \mathrm{V}$, by what percentage does the heat output of the heater drop? (Assume the resistance does not change.) (b) If you took the variation of resistance with temperature into account, would the actual drop in heat output be larger or smaller than calculated in part (a)?
Chelsea inadvertently bumps into a set of batteries with an emf of $100.0 \mathrm{V}\( that can supply a maximum power of \)5.0 \mathrm{W} .$ If the resistance between the points where she contacts the batteries is $1.0 \mathrm{k} \Omega,$ how much current passes through her?
A galvanometer has a coil resistance of \(34.0 \Omega .\) It is to be made into a voltmeter with a full-scale deflection equal to \(100.0 \mathrm{V}\). If the galvanometer deflects full scale for a current of \(0.120 \mathrm{mA},\) what size resistor should be placed in series with the galvanometer?
A Vespa scooter and a Toyota automobile might both use a \(12-\mathrm{V}\) battery, but the two batteries are of different sizes and can pump different amounts of charge. Suppose the scooter battery can pump 4.0 kC of charge and the automobile battery can pump \(30.0 \mathrm{kC}\) of charge. How much energy can each battery deliver, assuming the batteries are ideal?
The starter motor in a car draws \(220.0 \mathrm{A}\) of current from the \(12.0-\mathrm{V}\) battery for \(1.20 \mathrm{s}\). (a) How much charge is pumped by the battery? (b) How much electric energy is supplied by the battery?
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