Circuits Problems

This section provides 100 problems to test your understanding of DC circuits, including Kirchhoff's laws, series and parallel resistor combinations, capacitors in circuits, RC circuits, and their applications. 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 circuit analysis, a key topic for JEE/NEET success.

Numerical Problems

1. A junction in a circuit has currents $I_1=5\text{A}$ and $I_2=3\text{A}$ entering, and $I_3=4\text{A}$ leaving. Calculate the current $I_4$ leaving the junction.

   • (a) $3.99\text{A}$
   • (b) $4.00\text{A}$
   • (c) $4.01\text{A}$
   • (d) $4.02\text{A}$

2. A battery with emf $\mathcal{E}=12\text{V}$ and internal resistance $r=0.5\mathrm{\Omega }$ drives a current $I=2\text{A}$. Calculate the terminal voltage of the battery.

   • (a) $10.99\text{V}$
   • (b) $11.00\text{V}$
   • (c) $11.01\text{V}$
   • (d) $11.02\text{V}$

3. Two resistors $R_1=6\mathrm{\Omega }$ and $R_2=9\mathrm{\Omega }$ are connected in series. Calculate the equivalent resistance.

   • (a) $14.99\mathrm{\Omega }$
   • (b) $15.00\mathrm{\Omega }$
   • (c) $15.01\mathrm{\Omega }$
   • (d) $15.02\mathrm{\Omega }$

4. Three resistors $R_1=3\mathrm{\Omega }$, $R_2=6\mathrm{\Omega }$, and $R_3=9\mathrm{\Omega }$ are connected in parallel. Calculate the equivalent resistance.

   • (a) $1.49\mathrm{\Omega }$
   • (b) $1.50\mathrm{\Omega }$
   • (c) $1.51\mathrm{\Omega }$
   • (d) $1.52\mathrm{\Omega }$

5. Two capacitors $C_1=3\mu \text{F}$ and $C_2=6\mu \text{F}$ are connected in series. Calculate the equivalent capacitance.

   • (a) $1.99\mu \text{F}$
   • (b) $2.00\mu \text{F}$
   • (c) $2.01\mu \text{F}$
   • (d) $2.02\mu \text{F}$

6. An RC circuit has $R=2000\mathrm{\Omega }$ and $C=5\mu \text{F}$. Calculate the time constant $\tau$.

   • (a) $0.0099\text{s}$
   • (b) $0.0100\text{s}$
   • (c) $0.0101\text{s}$
   • (d) $0.0102\text{s}$

7. An RC circuit with $C=10\mu \text{F}$, $R=1000\mathrm{\Omega }$, and $\mathcal{E}=15\text{V}$ is charging. Calculate the charge on the capacitor at $t=0.01\text{s}$.

   • (a) $9.48\times {10}^{-5}\text{C}$
   • (b) $9.49\times {10}^{-5}\text{C}$
   • (c) $9.50\times {10}^{-5}\text{C}$
   • (d) $9.51\times {10}^{-5}\text{C}$

8. A capacitor with $Q_0=80\mu \text{C}$, $C=4\mu \text{F}$, and $R=5000\mathrm{\Omega }$ is discharging. Calculate the voltage across the capacitor at $t=0.02\text{s}$.

   • (a) $7.36\text{V}$
   • (b) $7.37\text{V}$
   • (c) $7.38\text{V}$
   • (d) $7.39\text{V}$

9. A circuit loop has a battery $\mathcal{E}=20\text{V}$, resistor $R=5\mathrm{\Omega }$, and current $I=4\text{A}$. Apply Kirchhoff's loop rule to find the internal resistance $r$.

   • (a) $0.249\mathrm{\Omega }$
   • (b) $0.250\mathrm{\Omega }$
   • (c) $0.251\mathrm{\Omega }$
   • (d) $0.252\mathrm{\Omega }$

10. Two resistors $R_1=8\mathrm{\Omega }$ and $R_2=12\mathrm{\Omega }$ are in parallel. Calculate the equivalent resistance.

    • (a) $4.79\mathrm{\Omega }$
    • (b) $4.80\mathrm{\Omega }$
    • (c) $4.81\mathrm{\Omega }$
    • (d) $4.82\mathrm{\Omega }$

11. Three capacitors $C_1=2\mu \text{F}$, $C_2=4\mu \text{F}$, and $C_3=8\mu \text{F}$ are in parallel. Calculate the equivalent capacitance.

    • (a) $13.9\mu \text{F}$
    • (b) $14.0\mu \text{F}$
    • (c) $14.1\mu \text{F}$
    • (d) $14.2\mu \text{F}$

12. An RC circuit has $R=5000\mathrm{\Omega }$, $C=2\mu \text{F}$, $\mathcal{E}=24\text{V}$. Calculate the current at $t=0.01\text{s}$ during charging.

    • (a) $0.00176\text{A}$
    • (b) $0.00177\text{A}$
    • (c) $0.00178\text{A}$
    • (d) $0.00179\text{A}$

13. A discharging RC circuit has $Q_0=60\mu \text{C}$, $R=2000\mathrm{\Omega }$, $C=15\mu \text{F}$. Calculate the charge at $t=0.03\text{s}$.

    • (a) $22.12\mu \text{C}$
    • (b) $22.13\mu \text{C}$
    • (c) $22.14\mu \text{C}$
    • (d) $22.15\mu \text{C}$

14. A junction has currents $I_1=7\text{A}$ and $I_2=2\text{A}$ entering, and $I_3=5\text{A}$ leaving. Calculate $I_4$ (leaving).

    • (a) $3.99\text{A}$
    • (b) $4.00\text{A}$
    • (c) $4.01\text{A}$
    • (d) $4.02\text{A}$

15. A battery with $\mathcal{E}=18\text{V}$, $r=0.2\mathrm{\Omega }$ drives $I=5\text{A}$. Calculate the terminal voltage.

    • (a) $16.99\text{V}$
    • (b) $17.00\text{V}$
    • (c) $17.01\text{V}$
    • (d) $17.02\text{V}$

16. Two resistors $R_1=10\mathrm{\Omega }$ and $R_2=15\mathrm{\Omega }$ are in series, with total current $I=2\text{A}$. Calculate the voltage across $R_1$.

    • (a) $19.99\text{V}$
    • (b) $20.00\text{V}$
    • (c) $20.01\text{V}$
    • (d) $20.02\text{V}$

17. Three resistors $R_1=4\mathrm{\Omega }$, $R_2=8\mathrm{\Omega }$, $R_3=12\mathrm{\Omega }$ are in parallel, with total $I=6\text{A}$. Calculate the current through $R_1$.

    • (a) $2.99\text{A}$
    • (b) $3.00\text{A}$
    • (c) $3.01\text{A}$
    • (d) $3.02\text{A}$

18. An RC circuit has $R=1000\mathrm{\Omega }$, $C=1\mu \text{F}$. Calculate the time for the charge to reach 50% of its final value during charging.

    • (a) $6.92\times {10}^{-4}\text{s}$
    • (b) $6.93\times {10}^{-4}\text{s}$
    • (c) $6.94\times {10}^{-4}\text{s}$
    • (d) $6.95\times {10}^{-4}\text{s}$

19. A circuit has $R_1=5\mathrm{\Omega }$ and $R_2=10\mathrm{\Omega }$ in series, then in parallel with $R_3=15\mathrm{\Omega }$. Calculate the equivalent resistance.

    • (a) $9.99\mathrm{\Omega }$
    • (b) $10.00\mathrm{\Omega }$
    • (c) $10.01\mathrm{\Omega }$
    • (d) $10.02\mathrm{\Omega }$

20. Two capacitors $C_1=1\mu \text{F}$ and $C_2=2\mu \text{F}$ are in parallel, with total charge $Q=30\mu \text{C}$. Calculate the charge on $C_1$.

    • (a) $9.99\mu \text{C}$
    • (b) $10.00\mu \text{C}$
    • (c) $10.01\mu \text{C}$
    • (d) $10.02\mu \text{C}$

21. An RC circuit with $C=8\mu \text{F}$, $R=3000\mathrm{\Omega }$, $\mathcal{E}=12\text{V}$ is charging. Calculate the voltage across the resistor at $t=0.024\text{s}$.

    • (a) $4.43\text{V}$
    • (b) $4.44\text{V}$
    • (c) $4.45\text{V}$
    • (d) $4.46\text{V}$

22. A discharging RC circuit has $Q_0=100\mu \text{C}$, $R=1000\mathrm{\Omega }$, $C=20\mu \text{F}$. Calculate the current at $t=0.02\text{s}$.

    • (a) $-0.00184\text{A}$
    • (b) $-0.00185\text{A}$
    • (c) $-0.00186\text{A}$
    • (d) $-0.00187\text{A}$

23. A junction has $I_1=10\text{A}$ entering, $I_2=4\text{A}$ and $I_3=3\text{A}$ leaving. Calculate $I_4$ (entering).

    • (a) $2.99\text{A}$
    • (b) $3.00\text{A}$
    • (c) $3.01\text{A}$
    • (d) $3.02\text{A}$

24. A battery with $\mathcal{E}=6\text{V}$, $r=0.1\mathrm{\Omega }$ drives $I=10\text{A}$. Calculate the terminal voltage.

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

25. Two resistors $R_1=12\mathrm{\Omega }$ and $R_2=18\mathrm{\Omega }$ are in series, with total $V=30\text{V}$. Calculate the current through the circuit.

    • (a) $0.999\text{A}$
    • (b) $1.000\text{A}$
    • (c) $1.001\text{A}$
    • (d) $1.002\text{A}$

26. Four resistors $R_1=2\mathrm{\Omega }$, $R_2=4\mathrm{\Omega }$, $R_3=6\mathrm{\Omega }$, $R_4=8\mathrm{\Omega }$ are in parallel. Calculate the equivalent resistance.

    • (a) $0.959\mathrm{\Omega }$
    • (b) $0.960\mathrm{\Omega }$
    • (c) $0.961\mathrm{\Omega }$
    • (d) $0.962\mathrm{\Omega }$

27. An RC circuit has $R=4000\mathrm{\Omega }$, $C=3\mu \text{F}$. Calculate the time for the charge to reach 75% of its final value during charging.

    • (a) $1.66\times {10}^{-2}\text{s}$
    • (b) $1.67\times {10}^{-2}\text{s}$
    • (c) $1.68\times {10}^{-2}\text{s}$
    • (d) $1.69\times {10}^{-2}\text{s}$

28. A discharging RC circuit has $Q_0=50\mu \text{C}$, $R=5000\mathrm{\Omega }$, $C=5\mu \text{F}$. Calculate the voltage across the resistor at $t=0.025\text{s}$.

    • (a) $-3.68\text{V}$
    • (b) $-3.69\text{V}$
    • (c) $-3.70\text{V}$
    • (d) $-3.71\text{V}$

29. Two capacitors $C_1=4\mu \text{F}$ and $C_2=8\mu \text{F}$ are in series, with total voltage $V=12\text{V}$. Calculate the voltage across $C_1$.

    • (a) $7.99\text{V}$
    • (b) $8.00\text{V}$
    • (c) $8.01\text{V}$
    • (d) $8.02\text{V}$

30. Three resistors $R_1=5\mathrm{\Omega }$, $R_2=10\mathrm{\Omega }$, $R_3=20\mathrm{\Omega }$ are in parallel, with total voltage $V=10\text{V}$. Calculate the total current.

    • (a) $3.49\text{A}$
    • (b) $3.50\text{A}$
    • (c) $3.51\text{A}$
    • (d) $3.52\text{A}$

31. In a spacecraft circuit, two resistors $R_1=2\mathrm{\Omega }$ and $R_2=3\mathrm{\Omega }$ are in series, then in parallel with $R_3=5\mathrm{\Omega }$. Calculate the equivalent resistance.

    • (a) $2.49\mathrm{\Omega }$
    • (b) $2.50\mathrm{\Omega }$
    • (c) $2.51\mathrm{\Omega }$
    • (d) $2.52\mathrm{\Omega }$

32. An RC circuit with $C=6\mu \text{F}$, $R=1500\mathrm{\Omega }$, $\mathcal{E}=18\text{V}$ is charging. Calculate the voltage across the capacitor at $t=0.009\text{s}$.

    • (a) $10.85\text{V}$
    • (b) $10.86\text{V}$
    • (c) $10.87\text{V}$
    • (d) $10.88\text{V}$

33. A discharging RC circuit has $Q_0=40\mu \text{C}$, $R=3000\mathrm{\Omega }$, $C=10\mu \text{F}$. Calculate the time for the charge to decay to 25% of its initial value.

    • (a) $4.15\times {10}^{-2}\text{s}$
    • (b) $4.16\times {10}^{-2}\text{s}$
    • (c) $4.17\times {10}^{-2}\text{s}$
    • (d) $4.18\times {10}^{-2}\text{s}$

34. A junction has $I_1=6\text{A}$ entering, $I_2=2\text{A}$ leaving, and $I_3=1\text{A}$ entering. Calculate $I_4$ (leaving).

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

35. A battery with $\mathcal{E}=24\text{V}$, $r=0.4\mathrm{\Omega }$ drives $I=8\text{A}$. Calculate the external resistance $R$.

    • (a) $2.59\mathrm{\Omega }$
    • (b) $2.60\mathrm{\Omega }$
    • (c) $2.61\mathrm{\Omega }$
    • (d) $2.62\mathrm{\Omega }$

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Conceptual Problems

36. What does Kirchhoff's first law represent?

• (a) Conservation of energy
• (b) Conservation of charge
• (c) Conservation of voltage
• (d) Conservation of resistance

37. What does Kirchhoff's second law represent?

• (a) Conservation of charge
• (b) Conservation of energy
• (c) Conservation of current
• (d) Conservation of capacitance

38. What happens to the equivalent resistance of resistors in series?

• (a) Less than the smallest resistance
• (b) Greater than the largest resistance
• (c) Equal to the smallest resistance
• (d) Equal to the largest resistance

39. What happens to the equivalent resistance of resistors in parallel?

• (a) Greater than the largest resistance
• (b) Less than the smallest resistance
• (c) Equal to the largest resistance
• (d) Equal to the smallest resistance

40. What is the role of a capacitor in a DC circuit immediately after the switch is closed?

• (a) Acts as an open circuit
• (b) Acts as a short circuit
• (c) Acts as a resistor
• (d) Acts as a battery

41. What is the unit of the time constant $\tau$ in an RC circuit?

• (a) Seconds
• (b) Ohms
• (c) Farads
• (d) Volts

42. What does a large time constant in an RC circuit indicate?

• (a) Faster charging/discharging
• (b) Slower charging/discharging
• (c) No charging/discharging
• (d) Infinite charging

43. What happens to the current in an RC circuit as the capacitor charges?

• (a) Increases exponentially
• (b) Decreases exponentially
• (c) Remains constant
• (d) Becomes zero immediately

44. What is the physical significance of internal resistance in a battery?

• (a) Increases the emf
• (b) Reduces the terminal voltage
• (c) Increases the terminal voltage
• (d) No effect on voltage

45. What is the dimension of the time constant $\tau$?

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

46. What does a zero potential difference around a loop indicate?

• (a) No current
• (b) Conservation of energy
• (c) No resistance
• (d) Infinite current

47. What is the significance of $\frac{1}{R_{\text{eq}}}=\sum \frac{1}{R_i}$?

• (a) Equivalent resistance in series
• (b) Equivalent resistance in parallel
• (c) Total current in series
• (d) Total voltage in parallel

48. What happens to the charge on capacitors in series?

• (a) Different on each capacitor
• (b) Same on each capacitor
• (c) Zero on each capacitor
• (d) Infinite on each capacitor

49. What does the exponential term $e^{-t/RC}$ represent in an RC circuit?

• (a) Rate of charging/discharging
• (b) Total charge on the capacitor
• (c) Total voltage in the circuit
• (d) Resistance of the circuit

50. How do RC circuits function in spacecraft timing systems?

• (a) Increase voltage
• (b) Provide time delays for control pulses
• (c) Reduce current
• (d) Increase resistance

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Derivation Problems

51. Derive Kirchhoff's first law based on the conservation of charge.

52. Derive Kirchhoff's second law based on the conservation of energy.

53. Derive the equivalent resistance for resistors in series $R_{\text{eq}}=R_1+R_2+\cdots +R_n$.

54. Derive the equivalent resistance for resistors in parallel $\frac{1}{R_{\text{eq}}}=\frac{1}{R_1}+\frac{1}{R_2}+\cdots +\frac{1}{R_n}$.

55. Derive the equivalent capacitance for capacitors in series $\frac{1}{C_{\text{eq}}}=\frac{1}{C_1}+\frac{1}{C_2}+\cdots +\frac{1}{C_n}$.

56. Derive the equivalent capacitance for capacitors in parallel $C_{\text{eq}}=C_1+C_2+\cdots +C_n$.

57. Derive the charging equation for an RC circuit $Q=C\mathcal{E}(1-e^{-t/RC})$.

58. Derive the discharging equation for an RC circuit $Q=Q_0{e}^{-t/RC}$.

59. Derive the terminal voltage of a battery with internal resistance $V=\mathcal{E}-Ir$.

60. Derive the current in an RC circuit during charging $I=\frac{\mathcal{E}}{R}{e}^{-t/RC}$.

61. Derive the voltage across the capacitor in a charging RC circuit $V_C=\mathcal{E}(1-e^{-t/RC})$.

62. Derive the time constant $\tau =RC$ and its significance in RC circuits.

63. Derive the voltage across the resistor in a discharging RC circuit $V_R=-\frac{Q_0}{C}{e}^{-t/RC}$.

64. Derive the current distribution in parallel resistors $I_i=\frac{V}{R_i}$.

65. Derive the charge distribution in series capacitors $Q$ is the same on each capacitor.

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NEET-style Conceptual Problems

66. What is the unit of electromotive force (emf)?

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

67. What does a positive potential difference across a resistor indicate in Kirchhoff's loop rule?

• (a) Current flows opposite to the direction of traversal
• (b) Current flows in the direction of traversal
• (c) No current flows
• (d) Infinite current

68. What is the relationship between currents in a series circuit?

• (a) Same current through all resistors
• (b) Different currents through each resistor
• (c) Zero current through all resistors
• (d) Infinite current through all resistors

69. What happens to the total capacitance in a parallel combination of capacitors?

• (a) Less than the smallest capacitance
• (b) Greater than the largest capacitance
• (c) Equal to the smallest capacitance
• (d) Equal to the largest capacitance

70. What does the time constant $\tau$ in an RC circuit represent?

• (a) Time to fully charge the capacitor
• (b) Time to reach ~63% of final charge during charging
• (c) Time to discharge completely
• (d) Time to reach 50% of final charge

71. What does the voltage across a capacitor in a DC circuit approach as time increases?

• (a) Zero
• (b) The emf of the battery
• (c) The resistance of the circuit
• (d) Infinite voltage

72. What is the role of Kirchhoff's laws in circuit analysis?

• (a) To increase resistance
• (b) To solve for unknown currents and voltages
• (c) To reduce current
• (d) To increase capacitance

73. What happens to the voltage across resistors in a parallel circuit?

• (a) Different for each resistor
• (b) Same for each resistor
• (c) Zero for each resistor
• (d) Infinite for each resistor

74. Why does the current in an RC circuit decrease during charging?

• (a) Due to the exponential term $e^{-t/RC}$
• (b) Due to increased resistance
• (c) Due to decreased capacitance
• (d) Due to increased voltage

75. What is the unit of internal resistance in a battery?

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

76. What does a constant voltage across a capacitor in a DC circuit indicate?

• (a) Capacitor is charging
• (b) Capacitor is fully charged
• (c) Capacitor is discharging
• (d) Capacitor is short-circuited

77. Which type of combination results in the same charge on each capacitor?

• (a) Parallel combination
• (b) Series combination
• (c) Mixed combination
• (d) No combination

78. What is the direction of current through a resistor in a loop when applying Kirchhoff's loop rule?

• (a) Always positive
• (b) Depends on the direction of traversal
• (c) Always negative
• (d) Zero

79. What does a pseudo-force do in a non-inertial frame for circuit analysis?

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

80. What is the dimension of emf?

• (a) $[\text{M}{\text{L}}^2{\text{T}}^{-3}{\text{A}}^{-1}]$
• (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 RC circuits in spacecraft control systems?

• (a) Increase voltage
• (b) Provide timing for control pulses
• (c) Reduce current
• (d) Increase resistance

82. What happens to the current through a capacitor in a DC circuit as time increases?

• (a) Increases to infinity
• (b) Decreases to zero
• (c) Remains constant
• (d) Oscillates

83. Why does the equivalent resistance in a series combination increase?

• (a) Due to $R_{\text{eq}}=\sum R_i$
• (b) Due to decreased current
• (c) Due to increased voltage
• (d) Due to decreased capacitance

84. What is the significance of $C\mathcal{E}(1-e^{-t/RC})$?

• (a) Charge on a capacitor during discharging
• (b) Charge on a capacitor during charging
• (c) Voltage across a resistor
• (d) Current in the circuit

85. What is the unit of equivalent resistance?

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

86. What does a zero current through a capacitor in a DC circuit indicate?

• (a) Capacitor is charging
• (b) Capacitor is fully charged
• (c) Capacitor is discharging
• (d) Capacitor is short-circuited

87. What is the physical significance of $\frac{\mathcal{E}-Ir}{I}$?

• (a) Internal resistance of a battery
• (b) External resistance in the circuit
• (c) Total current in the circuit
• (d) Total voltage in the circuit

88. Why does the voltage across a capacitor increase exponentially during charging?

• (a) Due to the term $1-e^{-t/RC}$
• (b) Due to increased resistance
• (c) Due to decreased capacitance
• (d) Due to increased current

89. What is the dimension of $\frac{Q}{C}$ in a capacitor circuit?

• (a) $[\text{M}{\text{L}}^2{\text{T}}^{-3}{\text{A}}^{-1}]$
• (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 Kirchhoff's junction rule apply to spacecraft electrical systems?

• (a) Increases voltage
• (b) Ensures current conservation at junctions
• (c) Reduces resistance
• (d) Increases capacitance

91. What is the role of internal resistance in a battery?

• (a) Increases the emf
• (b) Reduces the terminal voltage
• (c) Increases the terminal voltage
• (d) No effect on voltage

92. What does a high equivalent resistance in a parallel combination indicate?

• (a) Large individual resistances
• (b) Small individual resistances
• (c) No resistance
• (d) Infinite resistance

93. What is the physical significance of $\tau =RC$?

• (a) Resistance of the circuit
• (b) Time constant of an RC circuit
• (c) Charge on the capacitor
• (d) Voltage across the resistor

94. What is the dimension of $\frac{V}{R}$ in a circuit?

• (a) $[\text{A}]$
• (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 current through a resistor in a parallel circuit depend on its resistance?

• (a) Due to $I\propto \frac{1}{R}$
• (b) Due to increased voltage
• (c) Due to decreased capacitance
• (d) Due to increased charge

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NEET-style Numerical Problems

96. A junction has $I_1=8\text{A}$ entering, $I_2=3\text{A}$ leaving, and $I_3=2\text{A}$ leaving. Calculate $I_4$ (entering).

• (a) $2.99\text{A}$
• (b) $3.00\text{A}$
• (c) $3.01\text{A}$
• (d) $3.02\text{A}$

97. Two resistors $R_1=4\mathrm{\Omega }$ and $R_2=8\mathrm{\Omega }$ are in series. Calculate the equivalent resistance.

• (a) $11.99\mathrm{\Omega }$
• (b) $12.00\mathrm{\Omega }$
• (c) $12.01\mathrm{\Omega }$
• (d) $12.02\mathrm{\Omega }$

98. An RC circuit with $C=5\mu \text{F}$, $R=2000\mathrm{\Omega }$, $\mathcal{E}=10\text{V}$ is charging. Calculate the charge at $t=0.01\text{s}$.

• (a) $3.16\times {10}^{-5}\text{C}$
• (b) $3.17\times {10}^{-5}\text{C}$
• (c) $3.18\times {10}^{-5}\text{C}$
• (d) $3.19\times {10}^{-5}\text{C}$

99. A discharging RC circuit has $Q_0=30\mu \text{C}$, $R=1000\mathrm{\Omega }$, $C=10\mu \text{F}$. Calculate the voltage across the capacitor at $t=0.01\text{s}$.

• (a) $1.10\text{V}$
• (b) $1.11\text{V}$
• (c) $1.12\text{V}$
• (d) $1.13\text{V}$

100. A battery with $\mathcal{E}=9\text{V}$, $r=0.3\mathrm{\Omega }$ drives $I=6\text{A}$. Calculate the terminal voltage.
     - (a) $7.19\text{V}$
     - (b) $7.20\text{V}$
     - (c) $7.21\text{V}$
     - (d) $7.22\text{V}$

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