DC Circuits and Kirchhoffs Laws - Capacitance and Dielectrics

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Q1. What is the total resistance in a parallel circuit with three resistors of 2Ω, 3Ω, and 6Ω?

Solution:

1/R_eq = 1/R1 + 1/R2 + 1/R3 = 1/2 + 1/3 + 1/6 = 1. R_eq = 0.75Ω.

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Q2. Using Kirchhoff's Voltage Law, if a loop has a 12V source and two resistors of 3Ω and 4Ω, what is the voltage drop across the 3Ω resistor?

Solution:

Total resistance R = 3Ω + 4Ω = 7Ω. Total current I = V/R = 12V / 7Ω = 1.71A. Voltage drop across 3Ω = I * R = 1.71A * 3Ω = 5.14V.

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Q3. What is the voltage across a 10Ω resistor if the current flowing through it is 3A?

Solution:

Using Ohm's law, V = I * R = 3A * 10Ω = 30V.

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Q4. What is the potential difference across a capacitor of 8 µF charged with 16 µC?

Solution:

Voltage V = Q/C = 16 x 10^-6 C / 8 x 10^-6 F = 2V.

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Q5. In a circuit with a 24V battery and two resistors in series (8Ω and 4Ω), what is the voltage drop across the 4Ω resistor?

Solution:

Total resistance = 8Ω + 4Ω = 12Ω. Current I = V/R = 24V / 12Ω = 2A. Voltage drop across 4Ω = I * R = 2A * 4Ω = 8 V.

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Q6. In a circuit with a 24V battery and two resistors in series (4Ω and 8Ω), what is the voltage drop across the 8Ω resistor?

Solution:

Total resistance R = 4Ω + 8Ω = 12Ω. Current I = V/R = 24V / 12Ω = 2A. Voltage drop across 8Ω = I * R = 2A * 8Ω = 16V.

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Q7. If a capacitor of 5 µF is charged to a voltage of 10V, what is the stored energy?

Solution:

Energy stored, U = 0.5 * C * V² = 0.5 * 5 x 10^-6 F * (10V)² = 0.25 mJ.

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Q8. What is the potential difference across a capacitor of 8 µF if it stores a charge of 16 µC?

Solution:

Using the formula Q = C * V, we have V = Q / C = 16 x 10^-6 C / 8 x 10^-6 F = 2V.

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Q9. If a capacitor of 5 µF is charged to a voltage of 10V, what is the energy stored in the capacitor?

Solution:

Energy stored, U = 0.5 * C * V² = 0.5 * 5 x 10^-6 F * (10V)² = 0.25 mJ.

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Q10. What is the potential difference across a capacitor of 10 µF when it stores a charge of 20 µC?

Solution:

Using the formula Q = C * V, V = Q / C = 20 x 10^-6 C / 10 x 10^-6 F = 2 V.