Coulombs Law and Electric Field - Exam Prep Insights

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Coulombs Law and Electric Field - Transient Response in RC Circuits

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Coulombs Law and Electric Field - Transient Response in RC Circuits MCQ & Objective Questions

Coulombs Law and Electric Field, along with the Transient Response in RC Circuits, are crucial topics for students preparing for school and competitive exams. Understanding these concepts not only enhances your theoretical knowledge but also boosts your ability to tackle objective questions effectively. Practicing MCQs and important questions in this area can significantly improve your exam performance and confidence.

What You Will Practise Here

Understanding Coulombs Law and its applications in electric fields.
Key formulas related to electric fields and forces between charged particles.
The concept of capacitance and its role in RC circuits.
Transient response analysis in RC circuits, including time constants.
Graphical representation of voltage and current over time in RC circuits.
Common applications of RC circuits in real-world scenarios.
Important definitions and diagrams related to electric fields and RC circuits.

Exam Relevance

This topic is frequently featured in CBSE, State Boards, NEET, and JEE exams. Students can expect questions that test their understanding of Coulombs Law, the behavior of electric fields, and the transient response of RC circuits. Common question patterns include numerical problems, conceptual questions, and application-based scenarios, making it essential to master these concepts for effective exam preparation.

Common Mistakes Students Make

Confusing the direction of electric field lines and force on charges.
Misunderstanding the concept of time constant in RC circuits.
Overlooking the significance of initial and final conditions in transient analysis.
Neglecting to apply the correct formulas during calculations.

FAQs

Question: What is Coulombs Law?
Answer: Coulombs Law describes the force between two charged objects, stating that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

Question: How does the transient response in an RC circuit work?
Answer: The transient response in an RC circuit refers to how the voltage and current change over time when a voltage is applied or removed, characterized by an exponential rise or decay.

Now is the time to enhance your understanding of these concepts! Dive into practice MCQs and test your knowledge on Coulombs Law and Electric Field - Transient Response in RC Circuits. The more you practice, the better prepared you'll be for your exams!

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

A. 2 A
B. 0.5 A
C. 5 A
D. 10 A

Solution

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

Correct Answer: A — 2 A

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

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

Solution

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

Correct Answer: A — 2 A

Q. If a resistor of 10 Ω is connected in series with a 5 Ω resistor, what is the total resistance?

A. 15 Ω
B. 5 Ω
C. 10 Ω
D. 20 Ω

Solution

Total resistance in series is R_total = R1 + R2 = 10 Ω + 5 Ω = 15 Ω.

Correct Answer: A — 15 Ω

Q. In a parallel circuit with a 12 V battery, what is the voltage across each branch?

A. 12 V
B. 6 V
C. 24 V
D. 0 V

Solution

In a parallel circuit, the voltage across each branch is equal to the source voltage, which is 12 V.

Correct Answer: A — 12 V

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

A. Increases
B. Decreases
C. Remains constant
D. Oscillates

Solution

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

Correct Answer: B — Decreases

Q. In an RC circuit, what is the time constant if R = 2 kΩ and C = 10 µF?

A. 20 ms
B. 2 ms
C. 200 ms
D. 0.2 s

Solution

Time constant τ = R * C = (2000 Ω) * (10 x 10^-6 F) = 0.02 s = 20 ms.

Correct Answer: A — 20 ms

Q. In an RC circuit, what is the time constant if R = 4 kΩ and C = 10 µF?

A. 40 ms
B. 20 ms
C. 30 ms
D. 50 ms

Solution

Time constant τ = R * C = 4000 Ω * 10 x 10^-6 F = 40 ms.

Correct Answer: A — 40 ms

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

A. 50 µC
B. 100 µC
C. 25 µC
D. 75 µC

Solution

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

Correct Answer: A — 50 µC

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

A. 0.05 mC
B. 0.1 mC
C. 0.2 mC
D. 0.5 mC

Solution

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

Correct Answer: B — 0.1 mC

Q. What is the electric field inside a parallel plate capacitor with a potential difference of 100 V and plate separation of 0.01 m?

A. 10000 N/C
B. 1000 N/C
C. 100 N/C
D. 10 N/C

Solution

E = V/d = 100 V / 0.01 m = 10000 N/C.

Correct Answer: A — 10000 N/C

Q. What is the electric field strength at a distance of 0.2 m from a point charge of +5 µC?

A. 112.5 N/C
B. 112.5 kN/C
C. 25 N/C
D. 25 kN/C

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.

Correct Answer: A — 112.5 N/C

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

A. 1.125 N/C
B. 2.25 N/C
C. 0.5625 N/C
D. 0.75 N/C

Solution

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

Correct Answer: B — 2.25 N/C

Q. What is the electric potential energy of a system of two charges of +1 µC and -1 µC separated by 0.1 m?

A. -0.09 J
B. 0.09 J
C. 0.18 J
D. 0.36 J

Solution

Potential energy U = k * q1 * q2 / r = (8.99 x 10^9 N m²/C²) * (1 x 10^-6 C) * (-1 x 10^-6 C) / 0.1 m = -0.09 J.

Correct Answer: B — 0.09 J

Q. What is the electric potential energy of a system of two charges, +1 µC and -1 µC, separated by 0.1 m?

A. -0.09 J
B. 0.09 J
C. 0.18 J
D. 0.36 J

Solution

Potential energy U = k * q1 * q2 / r = (8.99 x 10^9 N m²/C²) * (1 x 10^-6 C) * (-1 x 10^-6 C) / 0.1 m = -0.09 J.

Correct Answer: A — -0.09 J

Q. What is the energy stored in a capacitor of 20 µF charged to 12 V?

A. 1.44 mJ
B. 0.12 mJ
C. 0.24 mJ
D. 0.48 mJ

Solution

Energy stored, U = 0.5 * C * V^2 = 0.5 * (20 x 10^-6 F) * (12 V)^2 = 1.44 mJ.

Correct Answer: A — 1.44 mJ

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

A. 2.4 µF
B. 10 µF
C. 1.5 µF
D. 3.6 µF

Solution

1/C_total = 1/C1 + 1/C2 = 1/4 + 1/6 = 5/12, thus C_total = 12/5 = 2.4 µF.

Correct Answer: A — 2.4 µF

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

A. 11 Ω
B. 10 Ω
C. 9 Ω
D. 8 Ω

Solution

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

Correct Answer: A — 11 Ω

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

A. 0.05 J
B. 0.05 C
C. 0.05 V
D. 0.05 F

Solution

The potential difference is simply the voltage, which is 5 V.

Correct Answer: C — 0.05 V

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

A. 40 V
B. 20 V
C. 10 V
D. 30 V

Solution

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

Correct Answer: A — 40 V

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

A. 10 µF
B. 24 µF
C. 2.4 µF
D. 0.4 µF

Solution

In parallel, C_eq = C1 + C2 = 4 µF + 6 µF = 10 µF.

Correct Answer: A — 10 µF

Q. What is the voltage across a capacitor after 3 time constants if it was charged to 12 V?

A. 12 V
B. 8 V
C. 4 V
D. 0 V

Solution

After 3 time constants, a capacitor is considered fully charged, so the voltage remains at 12 V.

Correct Answer: A — 12 V

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

A. 12 V
B. 8 V
C. 4 V
D. 0 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.

Correct Answer: B — 8 V

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