Electrostatics & Circuits Study for Competitive Exams

Electrostatics & Circuits

Coulombs Law and Electric Field Coulombs Law and Electric Field - Capacitance and Dielectrics Coulombs Law and Electric Field - Circuit Analysis Techniques Coulombs Law and Electric Field - Electric Field Problems Coulombs Law and Electric Field - Transient Response in RC Circuits Current, Resistance and Ohms Law Current, Resistance and Ohms Law - Capacitance and Dielectrics Current, Resistance and Ohms Law - Circuit Analysis Techniques Current, Resistance and Ohms Law - Electric Field Problems Current, Resistance and Ohms Law - Transient Response in RC Circuits DC Circuits and Kirchhoffs Laws DC Circuits and Kirchhoffs Laws - Capacitance and Dielectrics DC Circuits and Kirchhoffs Laws - Circuit Analysis Techniques DC Circuits and Kirchhoffs Laws - Electric Field Problems DC Circuits and Kirchhoffs Laws - Transient Response in RC Circuits Electric Potential and Capacitance Electric Potential and Capacitance - Capacitance and Dielectrics Electric Potential and Capacitance - Circuit Analysis Techniques Electric Potential and Capacitance - Electric Field Problems Electric Potential and Capacitance - Transient Response in RC Circuits Magnetic Fields and Electromagnetic Induction Magnetic Fields and Electromagnetic Induction - Capacitance and Dielectrics Magnetic Fields and Electromagnetic Induction - Circuit Analysis Techniques Magnetic Fields and Electromagnetic Induction - Electric Field Problems Magnetic Fields and Electromagnetic Induction - Transient Response in RC Circuits

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

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

A. 1.125 N/C
B. 2.25 N/C
C. 3.75 N/C
D. 4.5 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: A — 1.125 N/C

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

A. 1.12 N/C
B. 0.56 N/C
C. 2.25 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 = 1.12 N/C.

Correct Answer: A — 1.12 N/C

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Q. What is the electric field strength between two parallel plates separated by 0.1 m with a potential difference of 100 V?

A. 1000 N/C
B. 500 N/C
C. 100 N/C
D. 2000 N/C

Solution

The electric field (E) is given by E = V/d. Here, E = 100V / 0.1m = 1000 N/C.

Correct Answer: A — 1000 N/C

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Q. What is the electric potential (V) across a capacitor (C) charged to a charge (Q)?

A. V = Q/C
B. V = C/Q
C. V = Q*C
D. V = C^2/Q

Solution

The electric potential across a capacitor is given by the formula V = Q/C, where Q is the charge and C is the capacitance.

Correct Answer: A — V = Q/C

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Q. What is the electric potential (V) at a distance (r) from a point charge (Q)?

A. V = k * Q / r
B. V = k * Q * r
C. V = Q / (4 * π * ε * r^2)
D. V = Q / (4 * π * ε * r)

Solution

The electric potential due to a point charge is given by V = k * Q / r, where k is Coulomb's constant.

Correct Answer: A — V = k * Q / r

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Q. What is the electric potential at a point 1 m away from a +1 C charge?

A. 9 N/C
B. 1 V
C. 8.99 V
D. 0 V

Solution

Electric potential V = k * q / r = (8.99 x 10^9 N m²/C²) * (1 C) / (1 m) = 8.99 V.

Correct Answer: C — 8.99 V

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Q. What is the electric potential at a point 1 m away from a charge of +1 µC?

A. 9 kV
B. 1 kV
C. 0.9 kV
D. 0.1 kV

Solution

V = k * q / r = (8.99 x 10^9 N m²/C²) * (1 x 10^-6 C) / 1 m = 8.99 kV.

Correct Answer: A — 9 kV

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Q. What is the electric potential at a point 1 m away from a charge of +3 µC?

A. 9 V
B. 27 V
C. 18 V
D. 36 V

Solution

V = k * q / r = (8.99 x 10^9 N m²/C²) * (3 x 10^-6 C) / (1 m) = 26.97 V, approximately 27 V.

Correct Answer: B — 27 V

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Q. What is the electric potential at a point 3 m away from a charge of +1 µC?

A. 3000 V
B. 9000 V
C. 300 V
D. 900 V

Solution

V = k * q / r = (8.99 x 10^9 N m²/C²) * (1 x 10^-6 C) / 3 m = 3000 V.

Correct Answer: C — 300 V

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Q. What is the electric potential at a point 3 m away from a charge of +2 µC?

A. 0.6 V
B. 1.2 V
C. 2.4 V
D. 4.8 V

Solution

V = k * q / r = (8.99 x 10^9 N m²/C²) * (2 x 10^-6 C) / 3 m = 5.99 V.

Correct Answer: B — 1.2 V

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Q. What is the electric potential energy of a charge of +2 µC placed in an electric field of 500 N/C at a distance of 0.1 m?

A. 0.1 mJ
B. 0.2 mJ
C. 0.3 mJ
D. 0.4 mJ

Solution

Electric potential energy U = q * E * d = (2 x 10^-6 C) * (500 N/C) * (0.1 m) = 0.1 mJ.

Correct Answer: B — 0.2 mJ

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Q. What is the electric potential energy of a charge of +3 µC placed in an electric field of 2000 N/C at a distance of 0.5 m?

A. 3 J
B. 1.5 J
C. 0.3 J
D. 0.6 J

Solution

Potential energy U = q * E * d = (3 x 10^-6 C) * (2000 N/C) * (0.5 m) = 3 J.

Correct Answer: B — 1.5 J

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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

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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

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Q. What is the electric potential energy stored in a capacitor of 2 µF charged to 12 V?

A. 0.144 mJ
B. 0.288 mJ
C. 0.576 mJ
D. 0.072 mJ

Solution

U = 1/2 * C * V² = 1/2 * 2 x 10^-6 F * (12 V)² = 0.144 mJ.

Correct Answer: B — 0.288 mJ

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Q. What is the electric potential energy stored in a capacitor of capacitance 2 µF charged to 12 V?

A. 0.144 mJ
B. 0.024 mJ
C. 0.288 mJ
D. 0.072 mJ

Solution

Electric potential energy (U) is given by U = 1/2 CV^2. Here, U = 1/2 * 2 µF * (12 V)^2 = 0.144 mJ.

Correct Answer: A — 0.144 mJ

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Q. What is the electric potential energy stored in a capacitor with a capacitance of 2 µF charged to 12 V?

A. 0.144 mJ
B. 0.12 mJ
C. 0.24 mJ
D. 0.06 mJ

Solution

Electric potential energy (U) is given by U = 1/2 C V^2. Here, U = 1/2 * 2 µF * (12 V)^2 = 0.144 mJ.

Correct Answer: A — 0.144 mJ

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Q. What is the energy stored in a capacitor of 20 µF charged to 10 V?

A. 0.1 J
B. 0.2 J
C. 0.05 J
D. 0.15 J

Solution

Energy U = 0.5 * C * V² = 0.5 * 20 x 10^-6 F * (10 V)² = 0.1 J.

Correct Answer: B — 0.2 J

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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

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Q. What is the energy stored in a capacitor of 4 µF charged to a voltage of 12 V?

A. 0.288 mJ
B. 0.576 mJ
C. 0.144 mJ
D. 0.072 mJ

Solution

Using the formula U = 1/2 * C * V^2 = 1/2 * 4 x 10^-6 F * (12 V)^2 = 0.288 mJ.

Correct Answer: B — 0.576 mJ

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Q. What is the energy stored in a capacitor of 5 µF charged to 12V?

A. 0.36 mJ
B. 0.72 mJ
C. 0.12 mJ
D. 0.24 mJ

Solution

Energy U = 1/2 * C * V^2 = 1/2 * 5 x 10^-6 F * (12V)^2 = 0.36 mJ.

Correct Answer: A — 0.36 mJ

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Q. What is the energy stored in a capacitor of 5 µF charged to a voltage of 10 V?

A. 0.25 mJ
B. 0.5 mJ
C. 0.75 mJ
D. 1 mJ

Solution

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

Correct Answer: A — 0.25 mJ

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Q. What is the energy stored in a capacitor of 5 µF charged to a voltage of 12 V?

A. 0.36 mJ
B. 0.60 mJ
C. 0.72 mJ
D. 0.84 mJ

Solution

Energy stored U = 0.5 * C * V² = 0.5 * 5 x 10^-6 F * (12 V)² = 0.36 mJ.

Correct Answer: C — 0.72 mJ

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Q. What is the energy stored in a capacitor of 5µF charged to a voltage of 10V?

A. 0.25 mJ
B. 0.5 mJ
C. 1 mJ
D. 2.5 mJ

Solution

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

Correct Answer: B — 0.5 mJ

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Q. What is the energy stored in a capacitor of capacitance 5 µF charged to 10 V?

A. 0.25 mJ
B. 0.5 mJ
C. 0.75 mJ
D. 1 mJ

Solution

Energy (U) is given by U = 1/2 CV^2. Here, U = 1/2 * 5 µF * (10 V)^2 = 0.5 mJ.

Correct Answer: B — 0.5 mJ

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Q. What is the equivalent capacitance of two capacitors (3 µF and 6 µF) in series?

A. 2 µF
B. 1.5 µF
C. 9 µF
D. 18 µF

Solution

1/Ceq = 1/C1 + 1/C2 = 1/3 + 1/6 = 1/2. Therefore, Ceq = 2 µF.

Correct Answer: B — 1.5 µF

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Q. What is the equivalent capacitance of two capacitors of 4 µF and 6 µF connected 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 µF + 1/6 µF = 1.2 µF, so C_total = 2.4 µF.

Correct Answer: A — 2.4 µF

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Q. What is the equivalent capacitance of two capacitors, 2 µF and 3 µF, connected in series?

A. 1.2 µF
B. 5 µF
C. 0.6 µF
D. 6 µF

Solution

For capacitors in series, 1/C_eq = 1/C1 + 1/C2. Thus, 1/C_eq = 1/2 + 1/3 = 5/6. Therefore, C_eq = 6/5 = 1.2 µF.

Correct Answer: A — 1.2 µF

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Q. What is the equivalent capacitance of two capacitors, 3 µF and 6 µF, connected in series?

A. 2 µF
B. 1 µF
C. 9 µF
D. 4 µF

Solution

1/C_eq = 1/C1 + 1/C2 = 1/3 + 1/6 = 1/2. Therefore, C_eq = 2 µF.

Correct Answer: A — 2 µF

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Electrostatics & Circuits

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