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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

Two copper wires, one double the diameter of the other, have the same current flowing through them. If the thinner wire has a drift speed \(v_{1},\) and the thicker wire has a drift speed \(v_{2},\) how do the drift speeds of the charge carriers compare?
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 gold wire of 0.50 mm diameter has \(5.90 \times 10^{28} \mathrm{con}\) duction electrons/m". If the drift speed is \(6.5 \mu \mathrm{m} / \mathrm{s}\), what is the current in the wire?
A battery charger delivers a current of \(3.0 \mathrm{A}\) for \(4.0 \mathrm{h}\) to a \(12-\mathrm{V}\) storage battery. What is the total charge that passes through the battery in that time?
In the physics laboratory, Oscar measured the resistance between his hands to be \(2.0 \mathrm{k} \Omega .\) Being curious by nature, he then took hold of two conducting wires that were connected to the terminals of an emf with a terminal voltage of \(100.0 \mathrm{V} .\) (a) What current passes through Oscar? (b) If one of the conducting wires is grounded and the other has an alternate path to ground through a \(15-\Omega\) resistor (so that Oscar and the resistor are in parallel), how much current would pass through Oscar if the maximum current that can be drawn from the emf is \(1.00 \mathrm{A} ?\)
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