Question 1

Which of the following best describes electrical resistance in a conductor?

Accepted Answer

The opposition that a material offers to the flow of electric current.

Question 2

A copper wire of length $$L$$ and cross-sectional area $$A$$ has resistance $$R. If $$the wire is melted and recast to double its original length ($$2L) $$but with the same volume, what is the new resistance $$R'$$?

Accepted Answer

$$R' = 4R$$

Question 3

Which equation correctly relates resistance $$R to $$resistivity $$\rho$$, length $$L$$, and cross-sectional area $$A of a $$wire?

Accepted Answer

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

Question 4

A light bulb filament operates at a high temperature. Compared to when it is cold, its resistance when hot is:

Accepted Answer

Much higher

Question 5

The temperature dependence of resistance for a metal can be described by which of the following equations?

Accepted Answer

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

Question 6

Three resistors of $$2\ \Omega$$, $$4\ \Omega$$, and $$6\ \Omega$$ are connected in series. What is the total resistance?

Accepted Answer

$$12\ \Omega$$

Question 7

If the resistivity of a material is constant, which of the following will NOT affect the resistance of a wire made from that material?

Accepted Answer

Changing the color of the wire's insulation

Question 8

A resistor is added in series to a circuit containing a light bulb. What happens to the brightness of the bulb?

Accepted Answer

It decreases

Question 9

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

Accepted Answer

$$R[1 + \alpha \Delta T]$$

Question 10

Which of the following statements about resistors in series is correct?

Accepted Answer

The total resistance is equal to the sum of the individual resistances.

Question 11

A copper wire and an aluminum wire of equal length and cross-sectional area are connected in series. If the resistivity of copper is less than that of aluminum, which wire has the greater resistance?

Accepted Answer

Aluminum wire

Question 12

A 100 W incandescent light bulb operates at 120 V. What is the resistance of the filament when the bulb is on?

Accepted Answer

$$R = 144\ \Omega$$

Question 13

If a wire is stretched to three times its original length, assuming volume is conserved, what happens to its resistance?

Accepted Answer

It increases by a factor of 9

Question 14

Which of the following best explains why the resistance of a metal increases with temperature?

Accepted Answer

Increased lattice vibrations scatter electrons more, impeding their flow.

Question 15

A circuit contains three resistors in series: $$R_1 = 5$$\ \Omega$$, R_2$ = 10\ \Omega$$, and $$R_3 = 15$$\ \Omega$$. If the current through the circuit is 2$$\ \mathrm{A}$$, what is the voltage supplied by the battery?

Accepted Answer

$$60\ \mathrm{V}$$

Question 16

Which of the following is a correct unit for resistivity?

Accepted Answer

$$\Omega \cdot \mathrm{m}$$

Question 17

A wire has a resistance of $$10\ \Omega at$$ $$20^\circ \mathrm{C}. If $$the temperature coefficient of resistance is $$0.004/ ^\circ \mathrm{C}$$, what is its resistance at $$70^\circ \mathrm{C}$$?

Accepted Answer

$$12\ \Omega$$

Question 18

Which of the following real-world scenarios best illustrates the concept of resistance in a conductor?

Accepted Answer

Water flowing through a narrow pipe, slowing down due to friction with the walls.

Question 19

If the resistance of a wire is $$R at$$ $$T_0$$ and the temperature increases by $$\Delta T$$, which of the following would decrease the resistance?

Accepted Answer

Using a material with a negative temperature coefficient of resistance

Current, Resistance, and Resistor Series in Electric Circuits

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