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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 string of 25 decorative lights has bulbs rated at \(9.0 \mathrm{W}\) and the bulbs are connected in parallel. The string is connected to a \(120-\mathrm{V}\) power supply. (a) What is the resistance of each of these lights? (b) What is the current through each bulb? (c) What is the total current coming from the power supply? (d) The string of bulbs has a fuse that will blow if the current is greater than 2.0 A. How many of the bulbs can you replace with 10.4-W bulbs without blowing the fuse?
A gold wire and an aluminum wire have the same dimensions and carry the same current. The electron density (in electrons/cm \(^{3}\) ) in aluminum is three times larger than the density in gold. How do the drift speeds of the electrons in the two wires, \(v_{\mathrm{Au}}\) and \(v_{\mathrm{Al}},\) compare?
The label on a \(12.0-\mathrm{V}\) truck battery states that it is rated at 180.0 A-h (ampere-hours). Treat the battery as ideal. (a) How much charge in coulombs can be pumped by the battery? [Hint: Convert A to A-s.] (b) How much electric energy can the battery supply? (c) Suppose the radio in the truck is left on when the engine is not running. The radio draws a current of 3.30 A. How long does it take to drain the battery if it starts out fully charged?
What is the energy stored in a small battery if it can move \(675 \mathrm{C}\) through a potential difference of \(1.20 \mathrm{V} ?\)
Find the maximum current that a fully charged D-cell can supply - if only briefly-such that its terminal voltage is at least \(1.0 \mathrm{V}\). Assume an emf of \(1.5 \mathrm{V}\) and an internal resistance of \(0.10 \Omega .\)
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