Chapter Check · Electric Current, Drift Velocity and Ohm's Law

Question 1Foundation

1. A wire of cross-sectional area 4×10⁻⁶ m² carries a current of 20 A. Find the current density.

A 1×10⁷ A/m²B 5×10⁵ A/m²C 5×10⁶ A/m²D 2.5×10⁶ A/m²

Question 2Application

2. How many electrons flow past a cross-section per second in a wire carrying exactly 3.2 A? Use e=1.6×10⁻¹⁹ C.

A 6.25×10¹⁸ electrons/sB 3.2×10⁻¹⁹ electrons/sC 2×10¹⁸ electrons/sD 2×10¹⁹ electrons/s

Question 3Challenge

3. A conductor's resistance is measured to be 6 Ω. As current is increased from 2 A to 10 A, the voltage across it is measured at several points, and the V-I graph turns out to be a PERFECT straight line through the origin throughout this entire range. What can be concluded?

A R must be changing even though the graph looks straightB More data is needed regardless of the straight-line resultC The conductor IS ohmic across this entire current range, with R=6 Ω throughoutD The conductor cannot be ohmic since current varies so much

Question 4Application

4. Two wires, X and Y, made of the same metal (same n) carry the same current, but wire X has twice the cross-sectional area of wire Y. Compare their drift velocities.

A Drift velocity in X is half that in YB Drift velocity in X is double that in YC They are equalD Cannot be determined without more information

Question 5Challenge

5. A wire tapers uniformly so that its cross-sectional area varies with position x as A(x)=A₀(1+x) (x in metres, A₀=2×10⁻⁶ m²), carrying a steady current of 8 A. Find the current density at x=0 and at x=3 m.

A J(0)=1×10⁶ A/m², J(3)=4×10⁶ A/m²B J(0)=4×10⁶ A/m², J(3)=4×10⁶ A/m² (unchanged)C J(0)=8×10⁶ A/m², J(3)=2×10⁶ A/m²D J(0)=4×10⁶ A/m², J(3)=1×10⁶ A/m²

Question 6Foundation

6. A resistor of 13 Ω carries a current of 3 A. Find the voltage across it.

A 16 VB 4.33 VC 10 VD 39 V

Question 7Challenge

7. A wire's free electron density is 5×10²⁸ per m³ and its cross-sectional area is 2.5×10⁻⁶ m². If the drift velocity is measured to be 4×10⁻⁴ m/s, find the current flowing, then find how many electrons pass a given cross-section every second. Use e=1.6×10⁻¹⁹ C.

A I=8 A, 1.25×10¹⁹ electrons/sB I=1.25×10²³ A, 5×10¹⁹ electrons/sC I=8 A, 8×10¹⁹ electrons/sD I=8 A, 5×10¹⁹ electrons/s

Question 8Foundation

8. A conductor draws 3 A at 33 V, and 7 A at 77 V. Verify Ohm's Law and find R.

A Ohmic, R=11 ΩB Non-ohmicC Ohmic, R=7 ΩD Ohmic, R=22 Ω

Question 9Challenge

9. A wire carries a current that varies with time as I(t)=3t² (in amperes, t in seconds). Find the total charge that flows between t=0 and t=4 s.

A 192 CB 64 CC 48 CD 16 C

Question 10Application

10. A resistor's resistance is found to increase noticeably as more current is passed through it, due to self-heating. Strictly speaking, over this range of increasing current, is the resistor's V-I behavior perfectly ohmic?

A Yes, as long as V and I are both positiveB Cannot be determined without knowing the exact resistance valuesC No — R must stay constant for the behavior to be strictly ohmic, and here it's changing due to heatingD Yes, since V=IR can still be computed at each point

Question 11Challenge

11. A current of 4 A flows in one direction for 90 s, then reverses direction and flows at 3 A for the next 60 s. Taking the original direction as positive, find the NET charge transferred.

A −180 CB 180 CC 540 CD 360 C

Question 12Application

12. Inside a battery's external circuit, electrons flow from the negative terminal, through the wire, to the positive terminal. In which direction is conventional current considered to flow through this EXTERNAL circuit?

A From the negative terminal to the positive terminal, matching electron flowB There is no conventional current in this caseC Conventional current only exists inside the batteryD From the positive terminal, through the wire, to the negative terminal

Question 13Foundation

13. A wire has n=1×10²⁸ per m³, A=4×10⁻⁶ m², carrying a current of 3.2 A. Find the drift velocity. Use e=1.6×10⁻¹⁹ C.

A 5×10⁻⁵ m/sB 5×10⁻⁴ m/sC 1×10⁻⁴ m/sD 2.5×10⁻⁴ m/s

Question 14Foundation

14. A charge of 104 C flows through a wire in 8 seconds. Find the current.

A 13 AB 0.077 AC 832 AD 96 A

Question 15Application

15. A single wire carries the same current through a wide section (A=18×10⁻⁶ m²) and a narrow section (A=2×10⁻⁶ m²). Find the ratio v_d(narrow)/v_d(wide).

A 18B 9C 1/9D 4.5

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