Question 1

Two conductors are made of the same material and have the same length. Conductor A is a solid wire of diameter 1 m. Conductor B is a hollow tube of inside diameter 1 m and outside diameter 2 m. The ratio of their resistance, R_A/R_B, is: A) 1 B) C) 2 D) 3 E) 4

Accepted Answer

The answer of Two conductors are made of the same...

Question 2

Which of the following graphs best represents the current-voltage relationship of an incandescent light bulb? 
A) I
B) II
C) III
D) IV
E) V

Accepted Answer

The answer of Which of the following graphs best represents...

Question 3

Two substances are identical except that the electron mean free time for substance A is twice the electron mean free time for substance B. If the same electric field exists in both substances the electron drift speed in A is:
A) the same as in B
B) twice that in B
C) half that in B
D) four times that in B
E) one fourth that in B

Accepted Answer

The electron drift speed is directly proportional to the electron mean free time. Therefore, if the electron mean free time in substance A is twice that in substance B, the electron drift speed in A will be twice that in B.

Question 4

Which of the following graphs best represents the current-voltage relationship for a device that obeys Ohm's law? 
A) I
B) II
C) III
D) IV
E) V

Accepted Answer

Ohm's law states that the current passing through a conductor between two points is directly proportional to the voltage across the two points. This means that as the voltage increases or decreases, the current through the device also increases or decreases in a linear relationship. Graph II shows a linear relationship between current and voltage, indicating a device that obeys Ohm's law. The other graphs show non-linear relationships between current and voltage, which do not follow Ohm's law.

Question 5

For a cylindrical resistor made of ohmic material, the resistance does NOT depend on:
A) the current
B) the length
C) the cross-sectional area
D) the resistivity
E) the electron drift velocity

Accepted Answer

The answer of For a cylindrical resistor made of ohmic...

Question 6

For an ohmic substance the resistivity is the proportionality constant for:
A) current and potential difference
B) current and electric field
C) current density and potential difference
D) current density and electric field
E) potential difference and electric field

Accepted Answer

For an ohmic substance, the current density is directly proportional to the electric field, and the constant of proportionality is the resistivity. Therefore, the correct choice is D) current density and electric field.

Question 7

A wire is 1 m long and 1 *10^-6 m² in cross-sectional area. When connected to a potential difference of 2 V, a current of 4 A exists in the wire. The resistivity of this wire is: A) 2 * 10^-6 $\Omega$ .m B) 8 * 10^-6 $\Omega$ .m C) 1 * 10^-7 $\Omega$ .m D) 4 * 10^-7 $\Omega$ .m E) 5 *10^-7 $\Omega$ .m

Accepted Answer

The answer of A wire is 1 m long and...

Question 8

Five cylindrical wires are made of the same material. Their lengths and radii are  Rank the wires according to their resistances, least to greatest.
A) 1, 2, 3, 4, 5
B) 5, 4, 3, 2, 1
C) 1 and 2 tie, then 5, 3, 4
D) 1, 3, 4, 2, 5
E) 1, 2, 4, 3, 5

Accepted Answer

The answer of Five cylindrical wires are made of the...

Question 9

For an ohmic resistor, resistance is the proportionality constant for:
A) potential difference and electric field
B) current density and electric field
C) current and length
D) current and cross-sectional area
E) current and potential difference

Accepted Answer

Ohm's Law states that the current through an ohmic resistor is directly proportional to the potential difference across it. The proportionality constant is the resistance of the resistor, which means that the resistance is the proportionality constant for current and potential difference.

Question 10

For an ohmic substance, the resistivity depends on:
A) the electric field
B) the potential difference
C) the current density
D) the electron mean free time
E) the cross-sectional area of the sample

Accepted Answer

The resistivity of an ohmic substance is influenced by the electron mean free time, as it affects how easily electrons can move through the material, thus impacting its resistance. Other options like electric field, potential difference, current density, and cross-sectional area affect resistance or current flow but do not directly affect the material's inherent resistivity.

Question 11

The rate at which electrical energy is used may be measured in:
A) watt/second
B) watt·second
C) watt
D) joule·second
E) kilowatt·hour

Accepted Answer

The answer of The rate at which electrical energy is...

Question 12

A cylindrical copper rod has resistance R. It is reformed to twice its original length with no change of volume. Its new resistance is:
A) R/2
B) R
C) 2R
D) 4R
E) 8R

Accepted Answer

The resistance of a wire depends on its length, cross-sectional area, and resistivity. The resistivity of copper is typically constant over a range of temperatures and pressures.

When the cylindrical copper rod is reformed to twice its original length, its cross-sectional area is reduced by a factor of 2 (assuming the volume remains the same). Therefore, the resistance of the reformulated rod is:

R' = (2R) * (1/2)^2 = (2R/4) = R/2

Now, we have to consider the fact that the resistivity of the material will not change. To get the final resistance, we need to multiply the above result by 2 (since the length has been doubled).

R(final) = R/2 * 2 = R

Therefore, the new resistance is equal to the original resistance. However, it should be noted that the reformulation of the rod may have altered its other electrical properties (such as capacitance and inductance).

Question 13

Conductivity is: A) the same as resistivity, it is just more convenient to use for good conductors B) expressed in $\Omega$ ^-1 C) equal to 1/resistance D) expressed in ( $\Omega$ .m)^-1 E) not a meaningful quantity for an insulator

Accepted Answer

The answer of Conductivity is:
A) the same as resistivity, it...

Question 14

Of the following the copper conductor that has the least resistance is:
A) thin, long and hot
B) thick, short and cool
C) thick, long and hot
D) thin, short and cool
E) thin, short and hot

Accepted Answer

According to Ohm's law, resistance is directly proportional to the length of the conductor and inversely proportional to its cross-sectional area. So, a thick conductor will have lower resistance than a thin conductor. Also, resistance increases with temperature, so a cool conductor will have less resistance than a hot conductor. A short conductor will have less resistance than a long conductor. Therefore, the best choice is a thick, short, and cool conductor, which is option B.

Question 15

For an ohmic substance, the electron drift velocity is proportional to:
A) the cross-sectional area of the sample
B) the length of the sample
C) the mass of an electron
D) the electric field in the sample
E) none of the above

Accepted Answer

According to Ohm's law, the drift velocity of the electrons in an ohmic substance is proportional to the electric field in the sample. Therefore, the correct choice is option D. The other options, such as cross-sectional area, length, and mass of an electron, do not directly affect the drift velocity of the electrons in an ohmic substance.

Question 16

A certain wire has resistance R. Another wire, of the same material, has half the length and half the diameter of the first wire. The resistance of the second wire is:
A) R/4
B) R/2
C) R
D) 2R
E) 4R

Accepted Answer

The answer of A certain wire has resistance R. Another...

Question 17

A wire has an electric field of 6.2 V/m and carries a current density of 2.4 x 10⁸ A/m². What is its resistivity? A) 6.7 x 10^-10 $\Omega$ .m B) 1.5 x 10^-8 $\Omega$ .m C) 2.6 x 10^-8 $\Omega$ .m D) 3.9 x 10⁷ $\Omega$ .m E) 1.5 x 10⁹ $\Omega$ .m

Accepted Answer

We can use the formula relating resistivity (ρ), electric field (E), and current density (J): 
ρ = E/J 
Plugging in the given values: 
ρ = 6.2 V/m / (2.4 x 10^18 A/m^2) 
ρ = 2.6 x 10^-8 Ωm 
The closest option to this answer is C: 
2.6 x 10^-8 Ωm * 10^10 = 0.26 Ω*mm^2/m 
This matches the unit of resistivity, and is the best choice among the options given.

Question 18

Energy may be measured in:
A) kilowatt
B) joule·second
C) watt
D) watt·second
E) volt/ohm

Accepted Answer

Energy is measured in watt·seconds, among other units like joules. Kilowatts and watts are units of power, not energy. Volt/ohm is not a valid unit for energy; it simplifies to watts, which again, measure power. Joule·second is not a standard unit of energy; the joule alone is the correct unit for energy.

Question 19

A certain sample carries a current of 4 A when the potential difference is 2 V and a current of 10 A when the potential difference is 4 V. This sample:
A) obeys Ohm's law
B) has a resistance of 0.5  $\Omega$  at 2 V
C) has a resistance of 2  $\Omega$  at 2 V
D) has a resistance of 25 $\Omega$  at 2 V
E) does not have a resistance

Accepted Answer

The sample is not a constant resistor because its resistance changes with the applied potential difference. However, we can still calculate its resistance at a specific potential difference using Ohm's law, which states that resistance is equal to the ratio of potential difference to current. At 2 V, the resistance is 2/4 = 0.5 ohms.

Question 20

The resistance of a rod does NOT depend on:
A) its temperature
B) its material
C) its length
D) its conductivity
E) shape of its (fixed) cross-sectional area

Accepted Answer

The resistance of a rod depends on its temperature, material, length, and conductivity, but not on the shape of its (fixed) cross-sectional area, as long as the area remains constant. Resistance is primarily a function of material properties, dimensions, and temperature, but the shape of the cross-section does not affect resistance if the area is the same.

Quiz 26: Current and Resistance

Two conductors are made of the same material and have the same length. Conductor A is a solid wire of diameter 1 m. Conductor B is a hollow tube of inside diameter 1 m and outside diameter 2 m. The ratio of their resistance, RA/RB, is:

Which of the following graphs best represents the current-voltage relationship of an incandescent light bulb?

Two substances are identical except that the electron mean free time for substance A is twice the electron mean free time for substance B. If the same electric field exists in both substances the electron drift speed in A is:

Which of the following graphs best represents the current-voltage relationship for a device that obeys Ohm's law?

For a cylindrical resistor made of ohmic material, the resistance does NOT depend on:

For an ohmic substance the resistivity is the proportionality constant for:

A wire is 1 m long and 1 *10-6 m2 in cross-sectional area. When connected to a potential difference of 2 V, a current of 4 A exists in the wire. The resistivity of this wire is:

Five cylindrical wires are made of the same material. Their lengths and radii are Rank the wires according to their resistances, least to greatest.

For an ohmic resistor, resistance is the proportionality constant for:

For an ohmic substance, the resistivity depends on:

The rate at which electrical energy is used may be measured in:

A cylindrical copper rod has resistance R. It is reformed to twice its original length with no change of volume. Its new resistance is:

Conductivity is:

Of the following the copper conductor that has the least resistance is:

For an ohmic substance, the electron drift velocity is proportional to:

A certain wire has resistance R. Another wire, of the same material, has half the length and half the diameter of the first wire. The resistance of the second wire is:

A wire has an electric field of 6.2 V/m and carries a current density of 2.4 x 108 A/m2. What is its resistivity?

Energy may be measured in:

A certain sample carries a current of 4 A when the potential difference is 2 V and a current of 10 A when the potential difference is 4 V. This sample:

The resistance of a rod does NOT depend on:

Two conductors are made of the same material and have the same length. Conductor A is a solid wire of diameter 1 m. Conductor B is a hollow tube of inside diameter 1 m and outside diameter 2 m. The ratio of their resistance, R_A/R_B, is:

A wire is 1 m long and 1 *10^-6 m² in cross-sectional area. When connected to a potential difference of 2 V, a current of 4 A exists in the wire. The resistivity of this wire is:

A wire has an electric field of 6.2 V/m and carries a current density of 2.4 x 10⁸ A/m². What is its resistivity?