Q: A silver wire of diameter $$2.6\ \mathrm{mm}$$ transfers a charge of $$420\ \mathrm{C} in$$ $$80\ \mathrm{min}. $$What is the current in the wire?

$$I = \frac{420}{80 \times 60} = 0.088\ \mathrm{A}$$

Q: A copper wire of diameter $$2.05\ \mathrm{mm}$$ and length $$23.1\ \mathrm{m} is $$used in household wiring. Given the resistivity of copper is $$1.68 \times 10$$^{-8}$$\ \Omega\cdot\mathrm{m}$$, what is the resistance of the wire?

$$R = \frac{1.68 \times 10$$^{-8}$$ \times 23.1}{\pi (1.025 \times 10$$^{-3}$$)^2$$} = 0.12\ \Omega$

Q: A '100-W' European light bulb is rated for $$220\ \mathrm{V}. If $$used in the United States at $$120\ \mathrm{V}$$, what is its power output?

$$P = 100 \times \left(\frac{120}{220}\$$right)^2$$ = 29.8\ \mathrm{W}$$

Q: A GPS receiver operates at $$8.8\ \mathrm{V}$$ and draws $$0.15\ \mathrm{A}. $$How much electrical energy does it consume in $$1.5\ \mathrm{h}$$?

$$E = 8.8 \times 0.15 \times 1.5 \times 3600 = 7.1 \times 10^3$\ \mathrm{J}$$

Q: Which equation correctly relates the terminal voltage $$V_{\text{term}} of a $$battery to its emf $$\mathcal{E}$$, internal resistance $$r$$, and current $$I$$?

$$V_{\text{term}} = \mathcal{E} - Ir$$

Question 1

A battery with an emf of $$24.0\ \mathrm{V}$$ and internal resistance $$r is $$connected in series with a resistor $$R. $$The current in the circuit is $$4.00\ \mathrm{A}$$, and the terminal voltage of the battery is $$21.2\ \mathrm{V}. $$What is the value of the internal resistance $$r of $$the battery?

Accepted Answer

$$r = \frac{24.0 - 21.2}{4.00} = 0.70\ \Omega$$

Question 2

Given the same circuit, what is the resistance $$R of $$the external resistor?

Accepted Answer

$$R = \frac{21.2}{4.00} = 5.30\ \Omega$$

Question 3

A silver wire of diameter $$2.6\ \mathrm{mm}$$ transfers a charge of $$420\ \mathrm{C} in$$ $$80\ \mathrm{min}. $$What is the current in the wire?

Accepted Answer

$$I = \frac{420}{80 	imes 60} = 0.088\ \mathrm{A}$$

Question 4

A copper wire of diameter $$2.05\ \mathrm{mm}$$ and length $$23.1\ \mathrm{m} is $$used in household wiring. Given the resistivity of copper is $$1.68 	imes 10$$^{-8}$$\ \Omega\cdot\mathrm{m}$$, what is the resistance of the wire?

Accepted Answer

$$R = \frac{1.68 	imes 10$$^{-8}$$ 	imes 23.1}{\pi (1.025 	imes 10$$^{-3}$$)^2$$} = 0.12\ \Omega$

Question 5

A '100-W' European light bulb is rated for $$220\ \mathrm{V}. If $$used in the United States at $$120\ \mathrm{V}$$, what is its power output?

Accepted Answer

$$P = 100 	imes \left(\frac{120}{220}\$$right)^2$$ = 29.8\ \mathrm{W}$$

Question 6

How much current does the '100-W' European bulb draw when used at $$120\ \mathrm{V} in $$the United States?

Accepted Answer

$$I = \frac{120}{484} = 0.25\ \mathrm{A}$$

Question 7

A GPS receiver operates at $$8.8\ \mathrm{V}$$ and draws $$0.15\ \mathrm{A}. $$How much electrical energy does it consume in $$1.5\ \mathrm{h}$$?

Accepted Answer

$$E = 8.8 	imes 0.15 	imes 1.5 	imes 3600 = 7.1 	imes 10^3$\ \mathrm{J}$$

Question 8

Which equation correctly relates the terminal voltage $$V_{	ext{term}} of a $$battery to its emf $$\mathcal{E}$$, internal resistance $$r$$, and current $$I$$?

Accepted Answer

$$V_{	ext{term}} = \mathcal{E} - Ir$$

Question 9

If the drift velocity of electrons in a wire is doubled, what happens to the current, assuming all other factors remain constant?

Accepted Answer

The current doubles.

Question 10

A wire has a resistance $$R at $$temperature $$T_0. If $$the temperature increases and the resistivity increases by $$10\%$$, what is the new resistance?

Accepted Answer

$$R_{	ext{new}} = 1.1R$$

Question 11

Which of the following best explains why household wiring uses copper instead of silver, even though silver has lower resistivity?

Accepted Answer

Copper is much less expensive than silver, making it more practical for large-scale use.

Question 12

A wire of length $$L$$ and cross-sectional area $$A$$ carries a current $$I. If $$both $$L$$ and $$A$$ are doubled, what happens to the resistance?

Accepted Answer

The resistance remains the same.

Physics with Calculus: Current, Resistance, and EMF Study Guidance

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