DC Circuits and Kirchhoff's Laws for Exam Success

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DC Circuits and Kirchhoffs Laws

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

A. 0.125 mJ
B. 0.25 mJ
C. 0.5 mJ
D. 0.75 mJ

Solution

Energy stored U = 0.5 * C * V^2 = 0.5 * 10 x 10^-6 F * (5V)^2 = 0.125 mJ.

Correct Answer: B — 0.25 mJ

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Q. Using Kirchhoff's Voltage Law, what is the voltage drop across a 10Ω resistor if the total voltage in the loop is 20V and there is a 5Ω resistor in series?

A. 10V
B. 15V
C. 5V
D. 20V

Solution

Using KVL, V_total = V_R1 + V_R2. V_R1 = 20V - (I * 5Ω). I = V/R = 20V / 15Ω = 1.33 A. V_R1 = 10Ω * 1.33 A = 13.33V.

Correct Answer: A — 10V

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Q. What is the current through a 12Ω resistor connected to a 36V source?

A. 2A
B. 3A
C. 4A
D. 5A

Solution

Using Ohm's law, I = V/R = 36V / 12Ω = 3A.

Correct Answer: B — 3A

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Q. What is the electric field at a distance of 2 m from a point charge of +5 µC?

A. 0.56 N/C
B. 1.12 N/C
C. 2.24 N/C
D. 4.48 N/C

Solution

E = k * |q| / r^2 = (8.99 x 10^9 N m²/C²) * (5 x 10^-6 C) / (2 m)^2 = 1.12 N/C.

Correct Answer: C — 2.24 N/C

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Q. What is the equivalent resistance of three resistors, 2Ω, 3Ω, and 6Ω, connected in parallel?

A. 1Ω
B. 0.5Ω
C. 1.5Ω
D. 2.5Ω

Solution

1/R_total = 1/R1 + 1/R2 + 1/R3 = 1/2 + 1/3 + 1/6. R_total = 1.5Ω.

Correct Answer: C — 1.5Ω

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Q. What is the potential difference across a capacitor of 5 µF charged to 10V?

A. 5V
B. 10V
C. 15V
D. 20V

Solution

The potential difference across a capacitor is equal to the voltage it is charged to, which is 10V.

Correct Answer: B — 10V

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Q. What is the total capacitance of two capacitors, 4 µF and 6 µF, connected in series?

A. 2.4 µF
B. 10 µF
C. 1.5 µF
D. 3.0 µF

Solution

1/C_total = 1/C1 + 1/C2 = 1/4 + 1/6. C_total = 2.4 µF.

Correct Answer: A — 2.4 µF

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