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

Question 1Application

1. 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

Question 2Challenge

2. A wire carries a current that grows linearly with time: I(t)=2t (in amperes, t in seconds), starting from t=0. Find the total charge that flows between t=0 and t=5 s.

A 50 CB 5 CC 25 CD 10 C

Question 3Foundation

3. 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 4Foundation

4. 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 5Application

5. 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 6Challenge

6. A component's resistance R(T) increases with temperature: at 20°C, R=8 Ω; at 70°C, R=13 Ω. If it carries exactly 2 A at 70°C, find the voltage across it at that temperature, and state whether the device behaves as strictly ohmic across this temperature range.

A 13 V; not ohmicB 26 V; not strictly ohmic across this temperature range, since R itself changesC 16 V; ohmic across the rangeD 26 V; ohmic across the range, since V=IR was still used correctly

Question 7Foundation

7. 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 8Challenge

8. A wire narrows uniformly from area A₁=12×10⁻⁶ m² to area A₂=3×10⁻⁶ m² over its length, carrying a steady current of 6 A throughout. Find the current density J₂ at the narrow end, and the ratio J₂/J₁.

A J₂=2×10⁶ A/m², ratio J₂/J₁=4B J₂=5×10⁵ A/m², ratio=1C J₂=2×10⁶ A/m², ratio=0.25D J₂=8×10⁶ A/m², ratio=16

Question 9Foundation

9. 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 10Application

10. 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 11Foundation

11. 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 12Challenge

12. 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 13Challenge

13. 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 14Application

14. 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 15Application

15. 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

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