Coulombs Law and Electric Field - Transient Response in RC Circuits

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Q1. In a series RC circuit, what happens to the current as the capacitor charges?

Solution:

As the capacitor charges, the current decreases exponentially until it approaches zero.

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Q2. What is the electric field strength at a distance of 2 m from a +5 µC point charge?

Solution:

E = k * |q| / r^2 = (8.99 x 10^9 N m²/C²) * |5 x 10^-6 C| / (2 m)^2 = 1.125 N/C.

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Q3. What is the electric field strength at a distance of 0.2 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) / (0.2 m)^2 = 112.5 N/C.

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Q4. What is the charge stored in a capacitor of 5 µF when connected to a 10 V battery?

Solution:

Charge Q = C * V = 5 x 10^-6 F * 10 V = 0.05 mC.

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Q5. If a 12 V battery is connected to a 3 Ω resistor, what is the current flowing through the circuit?

Solution:

Using Ohm's law, I = V/R = 12 V / 3 Ω = 4 A.

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Q6. What is the potential difference across a 20 Ω resistor carrying a current of 2 A?

Solution:

Using Ohm's law, V = I * R = 2 A * 20 Ω = 40 V.

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Q7. What is the charge stored in a capacitor of 5 µF at a voltage of 10 V?

Solution:

Charge Q = C * V = 5 x 10^-6 F * 10 V = 50 µC.

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Q8. What is the equivalent resistance of three resistors of 2 Ω, 3 Ω, and 6 Ω in series?

Solution:

R_eq = R1 + R2 + R3 = 2 Ω + 3 Ω + 6 Ω = 11 Ω.

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Q9. What is the voltage across a capacitor after 3 time constants in an RC circuit with a supply voltage of 12 V?

Solution:

Voltage across capacitor V(t) = V0 * (1 - e^(-t/τ)). After 3τ, V(3τ) = 12 V * (1 - e^(-3)) ≈ 12 V * (1 - 0.05) ≈ 11.4 V.

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Q10. If a 10 V battery is connected to a 5 Ω resistor, what is the current flowing through the resistor?

Solution:

Using Ohm's law, I = V/R = 10 V / 5 Ω = 2 A.