Current and Resistance Problems

This section provides 100 problems to test your understanding of current and resistance, including calculations of electric current, current density, drift velocity, resistance, resistivity, temperature effects, and electrical power. Inspired by JEE Main, JEE Advanced, and NEET exam patterns, these problems are tailored for exam preparation, offering a mix of numerical, conceptual, and derivation-based challenges. NEET-style problems (66–100) are formatted as multiple-choice questions (MCQs) to match the exam’s objective format. Problems are organized by type to support progressive learning and build confidence in mastering current electricity, a key topic for JEE/NEET success.

Numerical Problems

1. A charge of $Q=20\text{C}$ passes through a conductor in $t=4\text{s}$. Calculate the electric current.

   • (a) $4.99\text{A}$
   • (b) $5.00\text{A}$
   • (c) $5.01\text{A}$
   • (d) $5.02\text{A}$

2. A wire with a cross-sectional area $A=3\times {10}^{-6}{\text{m}}^2$ carries a current $I=6\text{A}$. Calculate the current density.

   • (a) $1.99\times {10}^6{\text{A/m}}^2$
   • (b) $2.00\times {10}^6{\text{A/m}}^2$
   • (c) $2.01\times {10}^6{\text{A/m}}^2$
   • (d) $2.02\times {10}^6{\text{A/m}}^2$

3. A conductor with $A={10}^{-5}{\text{m}}^2$, $n=8\times {10}^{28}{\text{m}}^{-3}$, $q=1.6\times {10}^{-19}\text{C}$ carries $I=2\text{A}$. Calculate the drift velocity of electrons.

   • (a) $1.55\times {10}^{-5}\text{m/s}$
   • (b) $1.56\times {10}^{-5}\text{m/s}$
   • (c) $1.57\times {10}^{-5}\text{m/s}$
   • (d) $1.58\times {10}^{-5}\text{m/s}$

4. A resistor has a potential difference $V=15\text{V}$ and current $I=3\text{A}$. Calculate the resistance.

   • (a) $4.99\mathrm{\Omega }$
   • (b) $5.00\mathrm{\Omega }$
   • (c) $5.01\mathrm{\Omega }$
   • (d) $5.02\mathrm{\Omega }$

5. A wire has length $L=2\text{m}$, cross-sectional area $A=4\times {10}^{-7}{\text{m}}^2$, and resistivity $\rho =1.6\times {10}^{-8}\mathrm{\Omega }\cdot \text{m}$. Calculate the resistance.

   • (a) $0.0799\mathrm{\Omega }$
   • (b) $0.0800\mathrm{\Omega }$
   • (c) $0.0801\mathrm{\Omega }$
   • (d) $0.0802\mathrm{\Omega }$

6. A copper wire has ${\rho }_0=1.68\times {10}^{-8}\mathrm{\Omega }\cdot \text{m}$ at $T_0={20}^{\circ }\text{C}$, with $\alpha =0.0039{\text{K}}^{-1}$. Calculate $\rho$ at $T={60}^{\circ }\text{C}$.

   • (a) $1.83\times {10}^{-8}\mathrm{\Omega }\cdot \text{m}$
   • (b) $1.84\times {10}^{-8}\mathrm{\Omega }\cdot \text{m}$
   • (c) $1.85\times {10}^{-8}\mathrm{\Omega }\cdot \text{m}$
   • (d) $1.86\times {10}^{-8}\mathrm{\Omega }\cdot \text{m}$

7. A resistor has $R_0=20\mathrm{\Omega }$ at ${25}^{\circ }\text{C}$, with $\alpha =0.004{\text{K}}^{-1}$. Calculate $R$ at ${75}^{\circ }\text{C}$.

   • (a) $23.9\mathrm{\Omega }$
   • (b) $24.0\mathrm{\Omega }$
   • (c) $24.1\mathrm{\Omega }$
   • (d) $24.2\mathrm{\Omega }$

8. A resistor carries a current $I=4\text{A}$ through $R=2\mathrm{\Omega }$. Calculate the power dissipated.

   • (a) $31.9\text{W}$
   • (b) $32.0\text{W}$
   • (c) $32.1\text{W}$
   • (d) $32.2\text{W}$

9. A circuit has a potential difference $V=12\text{V}$ across a resistor $R=3\mathrm{\Omega }$ for $t=5\text{s}$. Calculate the energy dissipated.

   • (a) $239.9\text{J}$
   • (b) $240.0\text{J}$
   • (c) $240.1\text{J}$
   • (d) $240.2\text{J}$

10. A wire with a diameter of $1\text{mm}$ carries $I=2\text{A}$. Calculate the current density.

    • (a) $2.54\times {10}^6{\text{A/m}}^2$
    • (b) $2.55\times {10}^6{\text{A/m}}^2$
    • (c) $2.56\times {10}^6{\text{A/m}}^2$
    • (d) $2.57\times {10}^6{\text{A/m}}^2$

11. A conductor with $A=2\times {10}^{-6}{\text{m}}^2$, $n=6\times {10}^{28}{\text{m}}^{-3}$, $q=1.6\times {10}^{-19}\text{C}$ carries $I=1.5\text{A}$. Calculate the drift velocity.

    • (a) $7.79\times {10}^{-5}\text{m/s}$
    • (b) $7.80\times {10}^{-5}\text{m/s}$
    • (c) $7.81\times {10}^{-5}\text{m/s}$
    • (d) $7.82\times {10}^{-5}\text{m/s}$

12. A resistor has $V=24\text{V}$ and $I=8\text{A}$. Calculate the resistance.

    • (a) $2.99\mathrm{\Omega }$
    • (b) $3.00\mathrm{\Omega }$
    • (c) $3.01\mathrm{\Omega }$
    • (d) $3.02\mathrm{\Omega }$

13. A wire has $L=1.5\text{m}$, $A=5\times {10}^{-7}{\text{m}}^2$, $\rho =1.8\times {10}^{-8}\mathrm{\Omega }\cdot \text{m}$. Calculate the resistance.

    • (a) $0.0539\mathrm{\Omega }$
    • (b) $0.0540\mathrm{\Omega }$
    • (c) $0.0541\mathrm{\Omega }$
    • (d) $0.0542\mathrm{\Omega }$

14. A wire has ${\rho }_0=2.0\times {10}^{-8}\mathrm{\Omega }\cdot \text{m}$ at $T_0={20}^{\circ }\text{C}$, $\alpha =0.003{\text{K}}^{-1}$, at $T={50}^{\circ }\text{C}$. Calculate $\rho$.

    • (a) $2.17\times {10}^{-8}\mathrm{\Omega }\cdot \text{m}$
    • (b) $2.18\times {10}^{-8}\mathrm{\Omega }\cdot \text{m}$
    • (c) $2.19\times {10}^{-8}\mathrm{\Omega }\cdot \text{m}$
    • (d) $2.20\times {10}^{-8}\mathrm{\Omega }\cdot \text{m}$

15. A resistor has $R_0=15\mathrm{\Omega }$ at ${30}^{\circ }\text{C}$, $\alpha =0.002{\text{K}}^{-1}$, at ${80}^{\circ }\text{C}$. Calculate $R$.

    • (a) $15.29\mathrm{\Omega }$
    • (b) $15.30\mathrm{\Omega }$
    • (c) $15.31\mathrm{\Omega }$
    • (d) $15.32\mathrm{\Omega }$

16. A resistor has $V=20\text{V}$ across $R=5\mathrm{\Omega }$. Calculate the power dissipated.

    • (a) $79.9\text{W}$
    • (b) $80.0\text{W}$
    • (c) $80.1\text{W}$
    • (d) $80.2\text{W}$

17. A circuit has $I=3\text{A}$, $V=9\text{V}$ across a resistor for $t=10\text{s}$. Calculate the energy dissipated.

    • (a) $269.9\text{J}$
    • (b) $270.0\text{J}$
    • (c) $270.1\text{J}$
    • (d) $270.2\text{J}$

18. A charge of $Q=50\text{C}$ passes through a conductor in $t=10\text{s}$. Calculate the current.

    • (a) $4.99\text{A}$
    • (b) $5.00\text{A}$
    • (c) $5.01\text{A}$
    • (d) $5.02\text{A}$

19. A wire with $A={10}^{-6}{\text{m}}^2$ carries $I=1\text{A}$. Calculate the current density.

    • (a) $9.99\times {10}^5{\text{A/m}}^2$
    • (b) $1.00\times {10}^6{\text{A/m}}^2$
    • (c) $1.01\times {10}^6{\text{A/m}}^2$
    • (d) $1.02\times {10}^6{\text{A/m}}^2$

20. A conductor with $A={10}^{-4}{\text{m}}^2$, $n=5\times {10}^{28}{\text{m}}^{-3}$, $q=1.6\times {10}^{-19}\text{C}$ carries $I=0.5\text{A}$. Calculate the drift velocity.

    • (a) $6.24\times {10}^{-6}\text{m/s}$
    • (b) $6.25\times {10}^{-6}\text{m/s}$
    • (c) $6.26\times {10}^{-6}\text{m/s}$
    • (d) $6.27\times {10}^{-6}\text{m/s}$

21. A resistor has $V=18\text{V}$, $I=6\text{A}$. Calculate the resistance.

    • (a) $2.99\mathrm{\Omega }$
    • (b) $3.00\mathrm{\Omega }$
    • (c) $3.01\mathrm{\Omega }$
    • (d) $3.02\mathrm{\Omega }$

22. A wire has $L=3\text{m}$, $A=2\times {10}^{-6}{\text{m}}^2$, $\rho =1.5\times {10}^{-8}\mathrm{\Omega }\cdot \text{m}$. Calculate the resistance.

    • (a) $0.0224\mathrm{\Omega }$
    • (b) $0.0225\mathrm{\Omega }$
    • (c) $0.0226\mathrm{\Omega }$
    • (d) $0.0227\mathrm{\Omega }$

23. A wire has ${\rho }_0=1.5\times {10}^{-8}\mathrm{\Omega }\cdot \text{m}$ at $T_0={25}^{\circ }\text{C}$, $\alpha =0.0035{\text{K}}^{-1}$, at $T={65}^{\circ }\text{C}$. Calculate $\rho$.

    • (a) $1.71\times {10}^{-8}\mathrm{\Omega }\cdot \text{m}$
    • (b) $1.72\times {10}^{-8}\mathrm{\Omega }\cdot \text{m}$
    • (c) $1.73\times {10}^{-8}\mathrm{\Omega }\cdot \text{m}$
    • (d) $1.74\times {10}^{-8}\mathrm{\Omega }\cdot \text{m}$

24. A resistor has $R_0=30\mathrm{\Omega }$ at ${20}^{\circ }\text{C}$, $\alpha =0.0025{\text{K}}^{-1}$, at ${70}^{\circ }\text{C}$. Calculate $R$.

    • (a) $33.74\mathrm{\Omega }$
    • (b) $33.75\mathrm{\Omega }$
    • (c) $33.76\mathrm{\Omega }$
    • (d) $33.77\mathrm{\Omega }$

25. A resistor carries $I=5\text{A}$ through $R=4\mathrm{\Omega }$. Calculate the power dissipated.

    • (a) $99.9\text{W}$
    • (b) $100.0\text{W}$
    • (c) $100.1\text{W}$
    • (d) $100.2\text{W}$

26. A circuit has $V=15\text{V}$ across $R=6\mathrm{\Omega }$ for $t=8\text{s}$. Calculate the energy dissipated.

    • (a) $299.9\text{J}$
    • (b) $300.0\text{J}$
    • (c) $300.1\text{J}$
    • (d) $300.2\text{J}$

27. A wire with a diameter of $0.5\text{mm}$ carries $I=1.5\text{A}$. Calculate the current density.

    • (a) $7.63\times {10}^6{\text{A/m}}^2$
    • (b) $7.64\times {10}^6{\text{A/m}}^2$
    • (c) $7.65\times {10}^6{\text{A/m}}^2$
    • (d) $7.66\times {10}^6{\text{A/m}}^2$

28. A conductor with $A={10}^{-3}{\text{m}}^2$, $n={10}^{29}{\text{m}}^{-3}$, $q=1.6\times {10}^{-19}\text{C}$ carries $I=10\text{A}$. Calculate the drift velocity.

    • (a) $6.24\times {10}^{-7}\text{m/s}$
    • (b) $6.25\times {10}^{-7}\text{m/s}$
    • (c) $6.26\times {10}^{-7}\text{m/s}$
    • (d) $6.27\times {10}^{-7}\text{m/s}$

29. A wire has $L=0.5\text{m}$, $A={10}^{-6}{\text{m}}^2$, $\rho =2.5\times {10}^{-8}\mathrm{\Omega }\cdot \text{m}$. Calculate the resistance.

    • (a) $0.0124\mathrm{\Omega }$
    • (b) $0.0125\mathrm{\Omega }$
    • (c) $0.0126\mathrm{\Omega }$
    • (d) $0.0127\mathrm{\Omega }$

30. A wire has ${\rho }_0=1.8\times {10}^{-8}\mathrm{\Omega }\cdot \text{m}$ at $T_0={15}^{\circ }\text{C}$, $\alpha =0.004{\text{K}}^{-1}$, at $T={55}^{\circ }\text{C}$. Calculate $\rho$.

    • (a) $2.01\times {10}^{-8}\mathrm{\Omega }\cdot \text{m}$
    • (b) $2.02\times {10}^{-8}\mathrm{\Omega }\cdot \text{m}$
    • (c) $2.03\times {10}^{-8}\mathrm{\Omega }\cdot \text{m}$
    • (d) $2.04\times {10}^{-8}\mathrm{\Omega }\cdot \text{m}$

31. In a spacecraft circuit, a wire ($L=2\text{m}$, $A={10}^{-6}{\text{m}}^2$, $\rho =1.68\times {10}^{-8}\mathrm{\Omega }\cdot \text{m}$) carries $I=3\text{A}$. Calculate the power dissipated due to resistance.

    • (a) $0.149\text{W}$
    • (b) $0.150\text{W}$
    • (c) $0.151\text{W}$
    • (d) $0.152\text{W}$

32. A charge of $Q=100\text{C}$ passes through a conductor in $t=20\text{s}$. Calculate the current.

    • (a) $4.99\text{A}$
    • (b) $5.00\text{A}$
    • (c) $5.01\text{A}$
    • (d) $5.02\text{A}$

33. A wire with $A={10}^{-7}{\text{m}}^2$ carries $I=0.5\text{A}$. Calculate the current density.

    • (a) $4.99\times {10}^6{\text{A/m}}^2$
    • (b) $5.00\times {10}^6{\text{A/m}}^2$
    • (c) $5.01\times {10}^6{\text{A/m}}^2$
    • (d) $5.02\times {10}^6{\text{A/m}}^2$

34. A resistor has $V=30\text{V}$, $I=5\text{A}$. Calculate the power dissipated.

    • (a) $149.9\text{W}$
    • (b) $150.0\text{W}$
    • (c) $150.1\text{W}$
    • (d) $150.2\text{W}$

35. A circuit has $V=8\text{V}$ across $R=4\mathrm{\Omega }$ for $t=15\text{s}$. Calculate the energy dissipated.

    • (a) $239.9\text{J}$
    • (b) $240.0\text{J}$
    • (c) $240.1\text{J}$
    • (d) $240.2\text{J}$

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Conceptual Problems

36. What is electric current defined as?

• (a) Charge per unit area
• (b) Charge per unit time
• (c) Energy per unit charge
• (d) Potential difference per unit charge

37. What does the direction of conventional current represent?

• (a) Flow of electrons
• (b) Flow of positive charge
• (c) Flow of negative charge
• (d) No flow

38. What is the relationship between current density and electric field in a conductor?

• (a) $J\propto \frac{1}{E}$
• (b) $J\propto E$
• (c) $J$ is independent of $E$
• (d) $J\propto E^2$

39. What happens to the resistance of a wire if its length doubles?

• (a) Halves
• (b) Doubles
• (c) Quadruples
• (d) Quarters

40. What is the unit of resistivity in SI units?

• (a) $\mathrm{\Omega }\cdot \text{m}$
• (b) $\mathrm{\Omega }$
• (c) A/m²
• (d) W

41. What does a zero drift velocity indicate?

• (a) No current
• (b) Maximum current
• (c) No electric field
• (d) Infinite resistance

42. What is the physical significance of Ohm's law?

• (a) $V\propto \frac{1}{I}$
• (b) $V\propto I$
• (c) $V$ is independent of $I$
• (d) $I\propto R$

43. What does a high resistivity indicate?

• (a) Good conductor
• (b) Poor conductor
• (c) No conduction
• (d) Infinite conduction

44. What happens to the resistivity of a metal as temperature increases?

• (a) Decreases
• (b) Increases
• (c) Remains the same
• (d) Becomes zero

45. What is the dimension of electrical power?

• (a) $[\text{M}{\text{L}}^2{\text{T}}^{-3}]$
• (b) $[\text{M}\text{L}{\text{T}}^{-1}]$
• (c) $[\text{L}{\text{T}}^{-2}]$
• (d) $[\text{M}{\text{L}}^2{\text{T}}^{-1}]$

46. What does a low drift velocity in a conductor indicate?

• (a) High current
• (b) Low current density
• (c) High resistance
• (d) Low number density of carriers

47. What is the significance of $\rho \frac{L}{A}$?

• (a) Current in a conductor
• (b) Resistance of a conductor
• (c) Power dissipated
• (d) Energy stored

48. What happens to the power dissipated in a resistor if the current doubles?

• (a) Doubles
• (b) Halves
• (c) Quadruples
• (d) Quarters

49. What does the temperature coefficient of resistivity $\alpha$ indicate?

• (a) Rate of change of resistivity with temperature
• (b) Rate of change of current with temperature
• (c) Rate of change of power with temperature
• (d) Rate of change of energy with temperature

50. How does resistance in spacecraft wiring affect performance?

• (a) Increases current flow
• (b) Causes power loss as heat
• (c) Increases voltage
• (d) Decreases temperature

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Derivation Problems

51. Derive the expression for drift velocity $v_d=\frac{I}{nqA}$.

52. Derive the relationship between current density and electric field $J=\sigma E$.

53. Derive the resistance of a conductor $R=\rho \frac{L}{A}$.

54. Derive Ohm's law from the microscopic view of conduction.

55. Derive the temperature dependence of resistivity $\rho ={\rho }_0[1+\alpha (T-T_0)]$.

56. Derive the temperature dependence of resistance $R=R_0[1+\alpha (T-T_0)]$.

57. Derive the power dissipated in a resistor $P=I^{2}R$.

58. Derive the energy dissipated in a resistor $E=I^{2}Rt$.

59. Derive the relationship between current and charge $I=\frac{dQ}{dt}$.

60. Derive the expression for current density $J=\frac{I}{A}$.

61. Derive the conductance of a resistor $G=\frac{1}{R}$.

62. Derive the power in terms of voltage $P=\frac{V^2}{R}$.

63. Derive the resistivity of a material $\rho =\frac{E}{J}$.

64. Derive the relationship between drift velocity and electric field $v_d\propto E$.

65. Derive the total energy dissipated in a circuit $E=IVt$.

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NEET-style Conceptual Problems

66. What is the unit of electric current in SI units?

• (a) Ampere
• (b) Volt
• (c) Ohm
• (d) Watt

67. What does a negative temperature coefficient of resistivity indicate?

• (a) Metal
• (b) Semiconductor
• (c) Insulator
• (d) Superconductor

68. What is the relationship between power and resistance in a resistor?

• (a) $P\propto R$
• (b) $P\propto \frac{1}{R}$ (constant $V$)
• (c) $P$ is independent of $R$
• (d) $P\propto R^2$

69. What happens to the drift velocity if the current doubles?

• (a) Doubles
• (b) Halves
• (c) Quadruples
• (d) Quarters

70. What is the dimension of resistance?

• (a) $[\text{M}{\text{L}}^2{\text{T}}^{-3}{\text{A}}^{-2}]$
• (b) $[\text{M}\text{L}{\text{T}}^{-1}]$
• (c) $[\text{L}{\text{T}}^{-2}]$
• (d) $[\text{M}{\text{L}}^2{\text{T}}^{-1}]$

71. What does the cross-sectional area of a wire affect?

• (a) Current density
• (b) Electric field
• (c) Potential difference
• (d) Power dissipated

72. What is the role of temperature in the resistivity of a metal?

• (a) Decreases resistivity
• (b) Increases resistivity
• (c) No effect
• (d) Reduces current

73. What happens to the resistance of a wire in a series circuit?

• (a) Same for all wires
• (b) Depends on wire properties
• (c) Zero for all wires
• (d) Infinite for all wires

74. Why does the power dissipated in a resistor depend on $I^2$?

• (a) Due to $P=I^{2}R$
• (b) Due to symmetry
• (c) Due to field lines
• (d) Due to charge quantization

75. What is the unit of the temperature coefficient of resistivity?

• (a) ${\text{K}}^{-1}$
• (b) $\mathrm{\Omega }\cdot \text{m}$
• (c) A
• (d) W

76. What does a constant current through a resistor indicate?

• (a) Variable voltage
• (b) Constant voltage (ohmic)
• (c) Variable resistance
• (d) Zero resistance

77. Which material typically has a positive temperature coefficient of resistivity?

• (a) Semiconductor
• (b) Metal
• (c) Insulator
• (d) Superconductor

78. What is the direction of conventional current in a circuit?

• (a) From negative to positive
• (b) From positive to negative
• (c) Random
• (d) No direction

79. What does a pseudo-force do in a non-inertial frame for current calculations?

• (a) Affects perceived current
• (b) Affects charge distribution
• (c) Creates power
• (d) Reduces resistance

80. What is the dimension of energy dissipated in a resistor?

• (a) $[\text{M}{\text{L}}^2{\text{T}}^{-2}]$
• (b) $[\text{M}\text{L}{\text{T}}^{-1}]$
• (c) $[\text{L}{\text{T}}^{-2}]$
• (d) $[\text{M}{\text{L}}^2{\text{T}}^{-1}]$

81. What is the role of resistance in spacecraft circuits?

• (a) Reduces current flow
• (b) Increases power loss as heat
• (c) Increases voltage
• (d) Decreases temperature

82. What happens to the current density in a wire if the cross-sectional area doubles?

• (a) Doubles
• (b) Halves
• (c) Quadruples
• (d) Quarters

83. Why does the resistance of a conductor depend on its length?

• (a) Due to $R\propto L$
• (b) Due to symmetry
• (c) Due to field lines
• (d) Due to charge quantization

84. What is the significance of $IV$?

• (a) Resistance of a conductor
• (b) Power dissipated in a circuit
• (c) Current density
• (d) Drift velocity

85. What is the unit of energy dissipated in a resistor?

• (a) Joule
• (b) Volt
• (c) Ampere
• (d) Watt

86. What does a zero current density in a conductor indicate?

• (a) No current
• (b) Maximum current
• (c) No electric field
• (d) Infinite resistance

87. What is the physical significance of $\frac{n{e}^2\tau }{m}$?

• (a) Resistivity of a material
• (b) Conductivity of a material
• (c) Current density
• (d) Drift velocity

88. Why does the power dissipated in a resistor increase with increasing current?

• (a) Due to $P\propto I^2$
• (b) Due to symmetry
• (c) Due to field lines
• (d) Due to charge quantization

89. What is the dimension of $\rho$?

• (a) $[\text{M}{\text{L}}^3{\text{T}}^{-3}{\text{A}}^{-2}]$
• (b) $[\text{M}\text{L}{\text{T}}^{-1}]$
• (c) $[\text{L}{\text{T}}^{-2}]$
• (d) $[\text{M}{\text{L}}^2{\text{T}}^{-1}]$

90. How does temperature affect the performance of spacecraft wiring?

• (a) Increases current flow
• (b) Increases resistance, causing power loss
• (c) Reduces voltage
• (d) Decreases power

91. What is the role of the number density of charge carriers in drift velocity?

• (a) $v_d\propto n$
• (b) $v_d\propto \frac{1}{n}$
• (c) No dependence
• (d) Exponential dependence

92. What does a high current density in a wire indicate?

• (a) Low current
• (b) High current or small area
• (c) No current
• (d) Constant current

93. What is the physical significance of $\frac{V}{I}$?

• (a) Current density
• (b) Resistance of a conductor
• (c) Power dissipated
• (d) Energy stored

94. What is the dimension of $\frac{E}{J}$?

• (a) $[\text{M}{\text{L}}^3{\text{T}}^{-3}{\text{A}}^{-2}]$
• (b) $[\text{M}\text{L}{\text{T}}^{-1}]$
• (c) $[\text{L}{\text{T}}^{-2}]$
• (d) $[\text{M}{\text{L}}^2{\text{T}}^{-1}]$

95. Why does the resistivity of a semiconductor decrease with temperature?

• (a) Due to increased charge carriers
• (b) Due to symmetry
• (c) Due to field lines
• (d) Due to charge quantization

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NEET-style Numerical Problems

96. A charge of $Q=30\text{C}$ passes through a conductor in $t=6\text{s}$. Calculate the current.

• (a) $4.99\text{A}$
• (b) $5.00\text{A}$
• (c) $5.01\text{A}$
• (d) $5.02\text{A}$

97. A wire has $L=1\text{m}$, $A={10}^{-6}{\text{m}}^2$, $\rho =1.7\times {10}^{-8}\mathrm{\Omega }\cdot \text{m}$. Calculate the resistance.

• (a) $0.0169\mathrm{\Omega }$
• (b) $0.0170\mathrm{\Omega }$
• (c) $0.0171\mathrm{\Omega }$
• (d) $0.0172\mathrm{\Omega }$

98. A resistor has $R_0=10\mathrm{\Omega }$ at ${20}^{\circ }\text{C}$, $\alpha =0.003{\text{K}}^{-1}$, at ${50}^{\circ }\text{C}$. Calculate $R$.

• (a) $10.89\mathrm{\Omega }$
• (b) $10.90\mathrm{\Omega }$
• (c) $10.91\mathrm{\Omega }$
• (d) $10.92\mathrm{\Omega }$

99. A resistor carries $I=2\text{A}$ through $R=6\mathrm{\Omega }$. Calculate the power dissipated.

• (a) $23.9\text{W}$
• (b) $24.0\text{W}$
• (c) $24.1\text{W}$
• (d) $24.2\text{W}$

100. A circuit has $V=9\text{V}$ across $R=3\mathrm{\Omega }$ for $t=20\text{s}$. Calculate the energy dissipated.
     - (a) $539.9\text{J}$
     - (b) $540.0\text{J}$
     - (c) $540.1\text{J}$
     - (d) $540.2\text{J}$

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