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 equivalent capacitance of two capacitors, 4 µF and 6 µF, connected in series?

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

Solution

1/C_eq = 1/C1 + 1/C2 = 1/4 + 1/6 => C_eq = 2.4 µF.

Correct Answer: A — 2.4 µF

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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

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Q. What is the equivalent capacitance of two capacitors, C1 = 4μF and C2 = 6μF, connected in series?

A. 2.4μF
B. 3.6μF
C. 10μF
D. 24μF

Solution

For capacitors in series, 1/C_eq = 1/C1 + 1/C2 => C_eq = 2.4μF.

Correct Answer: A — 2.4μF

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Q. What is the equivalent resistance (R_eq) of two resistors (R1 and R2) in series?

A. R_eq = R1 + R2
B. R_eq = R1 * R2
C. R_eq = R1 / R2
D. R_eq = R1 - R2

Solution

The equivalent resistance of two resistors in series is R_eq = R1 + R2.

Correct Answer: A — R_eq = R1 + R2

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Q. What is the equivalent resistance (R_eq) of two resistors R1 and R2 in parallel?

A. 1/R_eq = 1/R1 + 1/R2
B. R_eq = R1 + R2
C. R_eq = R1 * R2
D. R_eq = R1 - R2

Solution

For resistors in parallel, the equivalent resistance is given by 1/R_eq = 1/R1 + 1/R2.

Correct Answer: A — 1/R_eq = 1/R1 + 1/R2

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Q. What is the equivalent resistance of three 4 Ω resistors in series?

A. 12 Ω
B. 8 Ω
C. 16 Ω
D. 4 Ω

Solution

R_eq = R1 + R2 + R3 = 4 Ω + 4 Ω + 4 Ω = 12 Ω.

Correct Answer: A — 12 Ω

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Q. What is the equivalent resistance of three resistors of 2 Ω, 3 Ω, and 5 Ω connected in series?

A. 10 Ω
B. 5 Ω
C. 8 Ω
D. 12 Ω

Solution

R_total = R1 + R2 + R3 = 2 Ω + 3 Ω + 5 Ω = 10 Ω.

Correct Answer: A — 10 Ω

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Q. What is the equivalent resistance of three resistors of 2 Ω, 3 Ω, and 5 Ω in series?

A. 10 Ω
B. 8 Ω
C. 5 Ω
D. 3 Ω

Solution

R_eq = R1 + R2 + R3 = 2 Ω + 3 Ω + 5 Ω = 10 Ω.

Correct Answer: A — 10 Ω

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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

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Q. What is the equivalent resistance of three resistors of 4 ohms, 6 ohms, and 12 ohms connected in series?

A. 22 ohms
B. 12 ohms
C. 10 ohms
D. 8 ohms

Solution

In series, R_eq = R1 + R2 + R3 = 4Ω + 6Ω + 12Ω = 22Ω.

Correct Answer: A — 22 ohms

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Q. What is the equivalent resistance of three resistors of 4 Ω, 6 Ω, and 12 Ω connected in series?

A. 22 Ω
B. 18 Ω
C. 16 Ω
D. 14 Ω

Solution

Equivalent resistance R_eq = R₁ + R₂ + R₃ = 4 Ω + 6 Ω + 12 Ω = 22 Ω.

Correct Answer: A — 22 Ω

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Q. What is the equivalent resistance of three resistors of 4 Ω, 6 Ω, and 12 Ω in series?

A. 22 Ω
B. 18 Ω
C. 16 Ω
D. 12 Ω

Solution

In series, R_eq = R1 + R2 + R3 = 4 Ω + 6 Ω + 12 Ω = 22 Ω.

Correct Answer: A — 22 Ω

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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 equivalent resistance of two resistors, 4 Ω and 6 Ω, connected in parallel?

A. 2.4 Ω
B. 10 Ω
C. 24 Ω
D. 1.5 Ω

Solution

1/R_total = 1/R1 + 1/R2 = 1/4 + 1/6 = 5/12, thus R_total = 12/5 Ω = 2.4 Ω.

Correct Answer: A — 2.4 Ω

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Q. What is the equivalent resistance of two resistors, R1 = 6Ω and R2 = 3Ω, connected in parallel?

A. 2Ω
B. 9Ω
C. 18Ω
D. 1.5Ω

Solution

In parallel, the equivalent resistance is given by 1/R_eq = 1/R1 + 1/R2, so 1/R_eq = 1/6 + 1/3 = 1/2, thus R_eq = 2Ω.

Correct Answer: A — 2Ω

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Q. What is the equivalent resistance of two resistors, R1 = 6Ω and R2 = 3Ω, connected in series?

A. 2Ω
B. 3Ω
C. 9Ω
D. 18Ω

Solution

In series, the equivalent resistance is R_eq = R1 + R2 = 6Ω + 3Ω = 9Ω.

Correct Answer: C — 9Ω

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Q. What is the expression for the capacitive reactance (Xc) in terms of frequency (f) and capacitance (C)?

A. Xc = 1/(2πfC)
B. Xc = 2πfC
C. Xc = 1/(fC)
D. Xc = 2πf/C

Solution

The capacitive reactance is given by Xc = 1/(2πfC), where f is the frequency and C is the capacitance.

Correct Answer: A — Xc = 1/(2πfC)

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Q. What is the expression for the total current (I) in a parallel circuit with two resistors (R1 and R2)?

A. I = I1 + I2
B. I = I1 * I2
C. I = I1 / I2
D. I = I1 - I2

Solution

In a parallel circuit, the total current is the sum of the currents through each resistor: I = I1 + I2.

Correct Answer: A — I = I1 + I2

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Q. What is the expression for the total energy stored in a capacitor (U) in terms of capacitance (C) and voltage (V)?

A. U = 1/2 * C * V^2
B. U = C * V^2
C. U = V / (2 * C)
D. U = C * V

Solution

The total energy stored in a capacitor is given by U = 1/2 * C * V^2.

Correct Answer: A — U = 1/2 * C * V^2

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Q. What is the final charge (Q) on a capacitor in an RC circuit when a voltage (V) is applied?

A. Q = CV
B. Q = V/R
C. Q = V^2/R
D. Q = I * t

Solution

The final charge on a capacitor when a voltage V is applied is given by Q = CV, where C is the capacitance.

Correct Answer: A — Q = CV

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Q. What is the final charge on a capacitor (Q) in an RC circuit after a long time if the voltage across it is 5V and the capacitance is 200 microfarads?

A. 0.001 C
B. 0.01 C
C. 0.0001 C
D. 0.1 C

Solution

The charge Q is given by Q = C * V = 200 x 10^-6 F * 5 V = 0.001 C.

Correct Answer: A — 0.001 C

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Q. What is the final voltage across a capacitor after it has been fully charged in an RC circuit?

A. 0V
B. V0
C. V0/2
D. V0/e

Solution

The final voltage across a capacitor after it has been fully charged in an RC circuit is V0, where V0 is the supply voltage.

Correct Answer: B — V0

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Q. What is the final voltage across a capacitor in a series RC circuit after a long time?

A. 0V
B. V0
C. V0/2
D. V0/e

Solution

The final voltage across a capacitor in a series RC circuit after a long time is V0, where V0 is the supply voltage.

Correct Answer: B — V0

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Q. What is the final voltage across the capacitor in a charging RC circuit if the applied voltage is 12V?

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

Solution

The final voltage across the capacitor in a charging RC circuit will equal the applied voltage, which is 12V.

Correct Answer: C — 12V

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Q. What is the force between two charges of +1 µC and +1 µC separated by 0.1 m?

A. 0.09 N
B. 0.18 N
C. 0.02 N
D. 0.04 N

Solution

F = k * |q1 * q2| / r² = (8.99 x 10^9 N m²/C²) * (1 x 10^-6 C)² / (0.1 m)² = 0.09 N.

Correct Answer: B — 0.18 N

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Q. What is the force between two charges of +1 µC and +1 µC separated by 1 m?

A. 8.99 N
B. 0.009 N
C. 0.089 N
D. 0.899 N

Solution

F = k * |q1 * q2| / r^2 = (8.99 x 10^9 N m²/C²) * (1 x 10^-6 C)² / (1 m)² = 8.99 N.

Correct Answer: A — 8.99 N

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Q. What is the force between two charges of +2 µC and -3 µC separated by a distance of 0.5 m?

A. -1.08 N
B. -0.72 N
C. 1.08 N
D. 0.72 N

Solution

Using Coulomb's law: F = k * |q1 * q2| / r^2 = (8.99 x 10^9 N m²/C²) * |(2 x 10^-6 C) * (-3 x 10^-6 C)| / (0.5 m)^2 = -1.08 N.

Correct Answer: A — -1.08 N

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Q. What is the force between two charges of 1 microcoulomb each, separated by a distance of 0.5 meters?

A. 0.36 N
B. 0.72 N
C. 0.18 N
D. 0.09 N

Solution

Using Coulomb's law, F = k * |q1 * q2| / r^2. Here, F = (8.99 x 10^9) * (1 x 10^-6)^2 / (0.5^2) = 0.36 N.

Correct Answer: A — 0.36 N

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Q. What is the force between two point charges of +2 µC and -3 µC separated by a distance of 0.5 m?

A. 1.2 N
B. 0.24 N
C. 0.48 N
D. 0.96 N

Solution

Using Coulomb's law, F = k * |q1 * q2| / r^2 = (8.99 x 10^9 N m²/C²) * |(2 x 10^-6 C) * (-3 x 10^-6 C)| / (0.5 m)^2 = 0.24 N.

Correct Answer: B — 0.24 N

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Q. What is the force between two point charges of +2 µC and -3 µC separated by a distance of 0.5 m in a vacuum?

A. -1.08 N
B. -0.72 N
C. 1.08 N
D. 0.72 N

Solution

Using Coulomb's law, F = k * |q1 * q2| / r^2 = (8.99 x 10^9 N m²/C²) * |(2 x 10^-6 C) * (-3 x 10^-6 C)| / (0.5 m)^2 = -1.08 N.

Correct Answer: A — -1.08 N

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Electrostatics & Circuits

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