Q: A copper wire has a cross-sectional area of $$2 \times 10$$^{-6}$$ \ \mathrm{m}^2$$ and carries a current of $$3 \ \mathrm{A}. If $$the number density of free electrons in copper is $$8.5 \times 10$$^{28}$$ \ \mathrm{m}^{-3}$$, what is the drift velocity of the electrons? (Charge of electron $$e = 1.6 \times 10$$^{-19}$$ \ \mathrm{C})$$

$$1.1 \times 10$$^{-4}$$ \ \mathrm{m/s}$$

Q: A metallic rod of length $$10 \ \mathrm{cm}$$ and cross-sectional area $$1.2 \times 1.2 \ \mathrm{mm}^2$$ has a resistivity of $$1 \times 10$$^{-7}$$ \ \Omega \cdot \mathrm{m}. $$What is its resistance along the length?

$$6.94 \times 10$$^{-4}$$ \ \Omega$$

Question 1

A copper wire has a cross-sectional area of $$2 	imes 10$$^{-6}$$ \ \mathrm{m}^2$$ and carries a current of $$3 \ \mathrm{A}. If $$the number density of free electrons in copper is $$8.5 	imes 10$$^{28}$$ \ \mathrm{m}^{-3}$$, what is the drift velocity of the electrons? (Charge of electron $$e = 1.6 	imes 10$$^{-19}$$ \ \mathrm{C})$$

Accepted Answer

$$1.1 	imes 10$$^{-4}$$ \ \mathrm{m/s}$$

Question 2

A 60 W light bulb is connected to a 120 V AC outlet. What is the resistance of the bulb's filament when operating at full power?

Accepted Answer

$$240 \ \Omega$$

Question 3

A metallic rod of length $$10 \ \mathrm{cm}$$ and cross-sectional area $$1.2 	imes 1.2 \ \mathrm{mm}^2$$ has a resistivity of $$1 	imes 10$$^{-7}$$ \ \Omega \cdot \mathrm{m}. $$What is its resistance along the length?

Accepted Answer

$$6.94 	imes 10$$^{-4}$$ \ \Omega$$

Question 4

If the temperature of a metal wire increases, what happens to its resistivity and why?

Accepted Answer

Resistivity increases because atomic vibrations increase, scattering electrons more.

Question 5

A 1200 W electric heater is used for 10 hours. If the cost of electricity is $$0.21$$ per kWh, what is the total cost to run the heater?

Accepted Answer

$$2.52$$

Question 6

A household circuit is rated for a maximum current of 15 A. Which combination of appliances will trip the circuit breaker if connected to a 120 V supply? (Lightbulb: 100 W, Electric heater: 1200 W, Stereo receiver: 350 W, Hair dryer: 1800 W)

Accepted Answer

Stereo receiver + Hair dryer

Question 7

Which of the following best describes the direction of conventional current in a metal wire?

Accepted Answer

It is the direction a positive charge would move, from high to low potential.

Question 8

A 100 W light bulb is labeled for 120 V AC. What is the peak voltage $$V_0$$ and peak power $$I_0$$ $$V_0$$ for this bulb?

Accepted Answer

$$170 \ \mathrm{V}, \ 200 \ \mathrm{W}$$

Question 9

If a wire's resistance is $$R at$$ $$20^\circC $$and the temperature coefficient of resistivity is $$\alpha$$, what is the resistance at temperature $$T$$?

Accepted Answer

$$R = R_0$ [1 + \alpha (T - T_0$)]$$

Question 10

A 0.0600 $$\Omega$$ extension cord carries 5.00 A. What is the power dissipated in the cord?

Accepted Answer

$$1.5 \ \mathrm{W}$$

Question 11

Which of the following statements about alternating current (AC) is correct?

Accepted Answer

The current and voltage vary sinusoidally with time.

Question 12

A person with dry skin (resistance $$200 \ \mathrm{k}\Omega) $$touches a 120 V source. What is the current through the body?

Accepted Answer

$$0.6 \ \mathrm{mA}$$

Question 13

Which of the following best explains why a fuse or circuit breaker is used in household circuits?

Accepted Answer

To break the circuit if the current exceeds a safe value, preventing overheating and fire.

Question 14

If the resistance of a wire is doubled while keeping the voltage constant, what happens to the current?

Accepted Answer

It is halved.

Question 15

A 100 W, 120 V light bulb is connected to a 240 V supply. What will happen to the bulb?

Accepted Answer

It will burn out almost instantly due to excessive power.

Question 16

Which formula gives the power dissipated in a resistor in terms of current and resistance?

Accepted Answer

$$P = I^2$ R$$

Question 17

A wire has a resistance $$R at$$ $$T_0. If $$the temperature increases by $$\Delta T$$, and the temperature coefficient is $$\alpha$$, what is the new resistivity?

Accepted Answer

$$\rho = \$$rho_0$$ [1 + \alpha \Delta T]$$

Question 18

Which of the following is a correct statement about the root mean square (rms) value of AC voltage?

Accepted Answer

$$V_{rms} = \frac{V_0$}{\sqrt{2}}$$

Question 19

A 10.0 A current flows through a microwave oven connected to a 120 V AC supply. What is the average power consumed?

Accepted Answer

$$1.20 \ \mathrm{kW}$$

Electric Currents and Circuits: Physics with Calculus Study Notes

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