A Level Physics

Question 1

A copper wire of cross-sectional area $`4.0 \times 10^(-6)` m 2$ carries a current of . The number of charge carriers per unit volume in copper is $10^(28)`$ , each carrying a charge of $10^(−19)`$ . Calculate the mean drift velocity of the charge carriers.

`I = A n v q`

`=> v = I / (A n q)`

`= 2.5 / (4.0 xx 10^-6 xx 8.4 xx 10^28 xx 1.6 xx 10^-19)`

`= 4.7 xx 10^-5 " m"."s"^-1`

Question 2

A car battery is labelled `50` Ah. This means that it can supply a current of `50` A for one hour.
a. For how long could the battery supply a continuous current of `200` A needed to start the car?
b. Calculate the charge that flows past a point in the circuit in this time.

a. Current increases by a factor of 4, therefore time decreases by a factor of 4.

So, time: `1/4 " hour" = "15 minutes"`

b. `ΔQ = IxxΔt = 200 xx 15 xx 60 = "180000 C"`

Question 3

Calculate the number of protons that would have a charge of one coulomb.
(Proton charge: `+1.6 × 10^(-19)` C).

`"Number of protons" = "total charge" / "charge on each proton"`

`1 / (1.6 xx 10^-19) = 6.3 xx 10^18 " protons"`

Question 4

Figure shows a circuit with two resistors, $`R_1`$ and $`R_2`$ , in series connected to a cell. The resistors are metal wires made of the same material and are of the same length. The diameter of $`R_1`$ is twice the diameter of $`R_2`$ . The drift velocity of the electrons in $`R_1`$ is $`v_1`$ , and the drift velocity of the electrons in $`R_2`$ is $`v_2`$ .

Which of the following answers gives the correct ratio `v_1/v_2`?

A. `0.25`.
B. `0.5`.
C. `1`.
D. `4`.

Answer: A
The diameter of $`R_1`$ is twice that of $`R_2`$
`d_1 = 2d_2 ⇒ r_1 = 2r, r_2 = r` $Drift velocity is inversely proportional to cross-sectional area: `v \propto 1 / A`$

Area of `R_1`: `A_1 = π (2r)^2 = 4 π r^2`
Area of `R_2`: `A_2 = π r^2`

Thus, `A_1 / A_2 = 4`

The ratio of drift velocities: `v_1 / v_2 = A_2 / A_1 = 1 / 4 = 0.25`

Question 5

What could not be used to create an electric current?
A. Alpha-particles.
B. Beta-particles.
C. Neutrons.
D. Protons.

Answer: C
A. Incorrect: They have +2 charge and can carry current.
B. Incorrect: These are charged electrons or positrons, both capable of creating current.
C. Correct: Neutrons have no electric charge, so they cannot generate an electric current.
D. Incorrect: Protons are positively charged and can form currents in conductive fluids.

Question 6

A fine mist of oil droplets is sprayed into air. As the oil droplets leave the nozzle of the spraying device they can become electrically charged. What is not a possible value for the charge on an oil droplet?
A. Zero.
B. `1 × 10^(–19)` C.
C. `4 × 10^(–19)` C.
D. `8 × 10^(–19)` C.

Answer: B
A. Incorrect: A droplet may have no net charge; this is entirely possible.
B. Correct:
Electric charge is quantized, meaning it must be an integer multiple of the elementary charge:
`Q = nxx e`, where n is an integer and `e = 1.6 xx 10^-19 " C"`
`1 × 10^(–19)` is not a multiple of `1.6 × 10^(–19) C`, so it is not physically possible. Therefore, it cannot be the charge on a droplet.
C. Incorrect: This equals , a valid multiple of the elementary charge.
D. Incorrect: This equals`5e`, a valid multiple of the elementary charge.

Question 7

The current I in a conductor is given by the equation: `I = Anvq`
What does the letter n represent in this equation?
A. Charge carried per charge carrier.
B. Number of charge carriers per unit area.
C. Number of charge carriers per unit volume.
D. Total mass of charge carriers per unit volume.

Answer: C
A. Incorrect: Represented by `q`, not `n`B. Incorrect: That would involve a 2D density, but `n`refers to volume, not area.
C. Correct:
`n` directly tells us how many charges exist in 1 cubic meter of conductor. In other words, `n` is number of charge carriers per unit volume.
D. Incorrect: The equation deals with electric charge, not mass.

Question 8

There is an electric current in a copper wire. Which statement describing the average drift speed of the charge carriers in the wire is correct?
A. It is nearly `3 xx10^8 " m"."s"^-1`
B. It is proportional to the cross-sectional area of the wire.
C. It is proportional to the length of the wire.
D. It is proportional to the magnitude of the current.

Answer: D
A. Incorrect: This is the speed of light, not the drift speed.
B. Incorrect: Dirft speed is inversely proportional to area, not directly.
C. Incorrect: Length does not appear in the drift speed formula; it affects resistance.
D. Correct:

The drift speed is given by the formula: `v = I / (A n q)`

So, drift velocity is directly proportional to current `I`.

Question 9

A length of wire RS has a circular cross-section. null =At end R of the wire, the cross-sectional area is `A`.
At end S of the wire, the cross-sectional area is `A/2`.
Charge `Q` takes time t to pass through end R of the wire. There is a constant electric current in the wire.
How much charge will pass through end S in a time interval of `t/4`.

A. `Q/8`

B. `Q/4`

C. `Q/2`

D. Q

Answer: B
Since current is constant across the wire.
At end R: `Q=Ixxt`
At end S, for time `t/4`: `Q_S = I xx(t/4) = Q / 4`

Question 10

Four point charges, each of charge Q, are placed on the edge of an insulating disc of radius r.
The disc rotates at a rate of n revolutions per unit time. null What is the equivalent electric current at the edge of the disc?
A. `4Qn`

B. `(4Q)/n`

C. `8pirQn`

D. `(2Qn)/(pir)`

Answer: A
A. Correct:
Each charge goes around the circle once per revolution.
If the disc makes $n$ revolutions per unit time, each charge contributes: `I = Q × n`
There are 4 charges, so total current is: `I = 4xxQxxn`
B. Incorrect: This inversely relates current to rotation rate, which is incorrect.
C. Incorrect: Introduces radius and π unnecessarily; those are used if we model current as a continuous rotating ring of charge.