Q: A battery with emf $$\mathcal{E}$$ and internal resistance $$r is $$connected to a load resistor $$R_{\text{load}}. $$What is the current $$I in $$the circuit?

$$I = \frac{\mathcal{E}}{R_{\text{load}} + r}$$

Q: The resistivity $$\rho of a $$metal at temperature $$T is $$given by $$\rho = \$$rho_0$$ [1 + \alpha (T - T_0$)]. If$$ $$\$$rho_0$$ = 1.72 \times 10$$^{-8}$$ \, \Omega \cdot m$$ for copper at $$T_0 = 20$$^\circ C$$ and $$\alpha = 3.9 \times $$10^{-3}$$ \, ^\circ $$C^{-1}$$, what is the resistivity at $$T = 120^\circ C$$?

$$2.39 \times 10$$^{-8}$$ \, \Omega \cdot m$$

Q: A material has a resistivity of $$2.0 \times 10$$^{-6}$$ \, \Omega \cdot m at$$ $$20^\circ C$$ and a temperature coefficient $$\alpha = 0.004 \, ^\circ C$$^{-1}$$. What is its resistivity at 70$$^\circ C$$?

$$2.4 \times 10$$^{-6}$$ \, \Omega \cdot m$$

Question 1

Two cylindrical resistors, R1 and R2, are made from the same material and have equal lengths. R1 has diameter $$d$$ and R2 has diameter $$2d. $$What is the ratio $$\frac{R_1$}{R_2$} of $$their resistances?

Accepted Answer

$$4$$

Question 2

If the same current flows through both resistors R1 and R2 (from the previous question), how do the average drift velocities $$v_1$$ and $$v_2 of $$the electrons compare?

Accepted Answer

$$v_1$$ \u003e $$v_2$$

Question 3

In the circuit shown in image 2, when bulb B is removed and the circuit is completed as in (b), compared to the brightness of bulb A in (a), bulb A in (b) is:

Accepted Answer

Brighter

Question 4

The resistance $$R of a $$wire of length $$l$$ and cross-sectional area $$A$$ made of a material with resistivity $$\rho is $$given by:

Accepted Answer

$$R = \frac{l}{A} \rho$$

Question 5

A battery with emf $$\mathcal{E}$$ and internal resistance $$r is $$connected to a load resistor $$R_{	ext{load}}. $$What is the current $$I in $$the circuit?

Accepted Answer

$$I = \frac{\mathcal{E}}{R_{	ext{load}} + r}$$

Question 6

The terminal voltage $$V of a $$battery with emf $$\mathcal{E}$$ and internal resistance $$r$$ delivering current $$I is$$:

Accepted Answer

$$V = \mathcal{E} - Ir$$

Question 7

Which of the following statements about resistivity and temperature is correct?

Accepted Answer

Resistivity usually increases with temperature, but for some substances it can decrease.

Question 8

The resistivity $$ho of a $$metal at temperature $$T is $$given by $$ho = \$$rho_0$$ [1 + \alpha (T - T_0$)]. If$$ $$\$$rho_0$$ = 1.72 	imes 10$$^{-8}$$ \, \Omega \cdot m$$ for copper at $$T_0 = 20$$^\circ C$$ and $$\alpha = 3.9 	imes $$10^{-3}$$ \, ^\circ $$C^{-1}$$, what is the resistivity at $$T = 120^\circ C$$?

Accepted Answer

$$2.39 	imes 10$$^{-8}$$ \, \Omega \cdot m$$

Question 9

A platinum wire has a resistance of $$11 \, \Omega at$$ $$20^\circ C. If $$the temperature coefficient $$\alpha is$$ $$3.93 	imes 10$$^{-3}$$ \, ^\circ C$$^{-1}$$, what is its resistance at 1000$$^\circ C$$?

Accepted Answer

$$53 \, \Omega$$

Question 10

Which material from the table in image 5 would be best for making a resistor whose resistance does not change much with temperature?

Accepted Answer

Manganin

Question 11

A wire of length $$l$$ and cross-sectional area $$A is $$made of a material with conductivity $$\sigma. $$What is the resistance $$R of $$the wire?

Accepted Answer

$$R = \frac{l}{A \sigma}$$

Question 12

If the length of a wire is doubled and its cross-sectional area is halved, by what factor does its resistance change?

Accepted Answer

It increases by a factor of 4

Question 13

A circuit consists of a battery with emf $$\mathcal{E}$$ and internal resistance $$r$$ connected to a load resistor $$R_{	ext{load}}. If$$ $$R_{	ext{load}} is $$much larger than $$r$$, what is the terminal voltage across the battery?

Accepted Answer

$$V \approx \mathcal{E}$$

Question 14

Which of the following best explains why the resistivity of metals increases with temperature?

Accepted Answer

The rate of collision of free charges with atoms increases due to greater atomic vibrations.

Question 15

A material has a resistivity of $$2.0 	imes 10$$^{-6}$$ \, \Omega \cdot m at$$ $$20^\circ C$$ and a temperature coefficient $$\alpha = 0.004 \, ^\circ C$$^{-1}$$. What is its resistivity at 70$$^\circ C$$?

Accepted Answer

$$2.4 	imes 10$$^{-6}$$ \, \Omega \cdot m$$

Question 16

Which of the following is the correct unit for resistivity?

Accepted Answer

$$\Omega \cdot m$$

Question 17

A copper wire has a resistance of $$5 \, \Omega at$$ $$20^\circ C. If $$the temperature increases to $$70^\circ C$$, what is the new resistance? ($$\alpha = 3.9 	imes 10$$^{-3}$$ \, ^\circ C$$^{-1}$$)

Accepted Answer

$$6.0 \, \Omega$$

Question 18

Which of the following statements about conductivity $$\sigma is $$correct?

Accepted Answer

$$\sigma is $$the reciprocal of resistivity $$\rho.$$

Question 19

A wire is made of a material with a temperature coefficient $$\alpha = 0.005 \, ^\circ C$$^{-1}$$. If the temperature increases by 40$$^\circ C$$, by what percentage does the resistance increase?

Accepted Answer

20%

Week 4 Lec. 2

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