DC Circuits and Kirchhoffs Laws

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Q1. What is the electric field at a distance of 2 m from a point charge of +5 µC?

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.

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Q2. What is the total capacitance of two capacitors, 4 µF and 6 µF, connected in series?

Solution:

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

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Q3. What is the equivalent resistance of three resistors, 2Ω, 3Ω, and 6Ω, connected in parallel?

Solution:

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

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Q4. 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?

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.

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Q5. What is the potential difference across a capacitor of 5 µF charged to 10V?

Solution:

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

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Q6. If a capacitor of 10 µF is charged to a voltage of 5V, what is the stored energy?

Solution:

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

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Q7. What is the current through a 12Ω resistor connected to a 36V source?

Solution:

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

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