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 force between two point charges of +3 µC and -2 µC separated by a distance of 0.5 m?

A. 1.2 N
B. 0.6 N
C. 0.4 N
D. 0.8 N

Solution

Using Coulomb's law, F = k * |q1 * q2| / r^2 = (8.99 x 10^9 N m²/C²) * |3 x 10^-6 C * -2 x 10^-6 C| / (0.5 m)² = 1.2 N.

Correct Answer: A — 1.2 N

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Q. What is the force on a charge of +1 µC placed in an electric field of 1000 N/C?

A. 0.001 N
B. 0.1 N
C. 1 N
D. 10 N

Solution

F = q * E = (1 x 10^-6 C) * (1000 N/C) = 0.001 N.

Correct Answer: B — 0.1 N

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Q. What is the force on a charge of +1 µC placed in an electric field of 500 N/C?

A. 0.5 N
B. 1 N
C. 2 N
D. 0.2 N

Solution

F = q * E = (1 x 10^-6 C) * (500 N/C) = 0.5 N.

Correct Answer: A — 0.5 N

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Q. What is the formula for calculating the current (I) in an RC circuit after a time (t) when a voltage (V) is applied?

A. I = V/R
B. I = V(1 - e^(-t/RC))
C. I = V/R * e^(-t/RC)
D. I = V * e^(-t/RC)

Solution

The current in an RC circuit after a time t is given by I = V(1 - e^(-t/RC)), where V is the voltage, R is the resistance, and C is the capacitance.

Correct Answer: B — I = V(1 - e^(-t/RC))

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Q. What is the formula for the charge (Q) on a capacitor at time t during charging in an RC circuit?

A. Q = C*V(1 - e^(-t/RC))
B. Q = C*V*e^(-t/RC)
C. Q = C*V*t
D. Q = C*V*t^2

Solution

The charge on a capacitor during charging in an RC circuit is given by Q = C*V(1 - e^(-t/RC)).

Correct Answer: A — Q = C*V(1 - e^(-t/RC))

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Q. What is the formula for the electric field (E) between two parallel plates separated by a distance (d) with a potential difference (V)?

A. E = V/d
B. E = d/V
C. E = V*d
D. E = d^2/V

Solution

The electric field between two parallel plates is given by E = V/d.

Correct Answer: A — E = V/d

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Q. What is the formula for the electric field (E) due to a point charge (Q) at a distance (r)?

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

Solution

The electric field due to a point charge is given by E = k * Q / r^2, where k is Coulomb's constant.

Correct Answer: A — E = k * Q / r^2

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Q. What is the formula for the energy stored in a capacitor?

A. U = 1/2 C V^2
B. U = C V
C. U = C V^2
D. U = 1/2 Q V

Solution

The energy (U) 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 formula for the total capacitance (C_total) of capacitors in series?

A. 1/C_total = 1/C1 + 1/C2
B. C_total = C1 + C2
C. C_total = C1 * C2
D. C_total = C1 - C2

Solution

For capacitors in series, the total capacitance is given by 1/C_total = 1/C1 + 1/C2.

Correct Answer: A — 1/C_total = 1/C1 + 1/C2

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Q. What is the magnetic field strength at a distance of 0.1 m from a long straight wire carrying a current of 5 A?

A. 0.1 T
B. 0.01 T
C. 0.05 T
D. 0.02 T

Solution

Using the formula B = (μ0 * I) / (2 * π * r), where μ0 = 4π x 10^-7 T m/A, B = (4π x 10^-7 * 5) / (2 * π * 0.1) = 0.01 T.

Correct Answer: B — 0.01 T

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Q. What is the potential difference (V) across a capacitor after it has been fully charged in an RC circuit?

A. V = 0
B. V = V0
C. V = R * I
D. V = C * I

Solution

After a capacitor is fully charged in an RC circuit, the potential difference across it is equal to the source voltage V = V0.

Correct Answer: B — V = V0

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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

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Q. What is the potential difference across a 10Ω resistor carrying a current of 3A?

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

Solution

Using Ohm's law, V = I * R = 3A * 10Ω = 30 V.

Correct Answer: C — 30 V

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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

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

A. 50 mJ
B. 0.05 J
C. 0.5 J
D. 5 J

Solution

Energy stored in a capacitor, U = 0.5 * C * V^2 = 0.5 * (5 x 10^-6 F) * (10 V)^2 = 0.05 J.

Correct Answer: B — 0.05 J

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

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

Solution

The potential difference across a capacitor is given by V = Q / C.

Correct Answer: A — V = Q / C

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Q. What is the potential difference across a capacitor if it has a capacitance of 5μF and stores a charge of 10μC?

A. 1V
B. 2V
C. 3V
D. 4V

Solution

The potential difference V across a capacitor is given by V = Q/C. Therefore, V = 10μC / 5μF = 2V.

Correct Answer: C — 3V

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Q. What is the potential difference across a capacitor if it stores 10 µC of charge and has a capacitance of 5 µF?

A. 2 V
B. 5 V
C. 10 V
D. 20 V

Solution

Using C = Q/V, we find V = Q/C = 10 µC / 5 µF = 2 V.

Correct Answer: A — 2 V

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Q. What is the potential difference across a capacitor if it stores 20 µC of charge and has a capacitance of 5 µF?

A. 4 V
B. 5 V
C. 2 V
D. 10 V

Solution

Using the formula V = Q/C, V = 20 µC / 5 µF = 4 V.

Correct Answer: A — 4 V

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

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

Solution

Energy stored in a capacitor U = 0.5 * C * V² = 0.5 * 10 x 10^-6 F * (5 V)² = 0.125 J.

Correct Answer: B — 0.1 J

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

A. 0.05 V
B. 0.5 V
C. 5 V
D. 50 V

Solution

The potential difference across a capacitor is equal to the voltage it is charged to, which is 5 V.

Correct Answer: C — 5 V

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Q. What is the potential difference across a capacitor of 10 µF when it stores a charge of 20 µC?

A. 2 V
B. 0.5 V
C. 1 V
D. 3 V

Solution

Using the formula Q = C * V, V = Q / C = 20 x 10^-6 C / 10 x 10^-6 F = 2 V.

Correct Answer: A — 2 V

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Q. What is the potential difference across a capacitor of 2 microfarads charged to 10 volts?

A. 20 mC
B. 0.02 C
C. 0.02 mC
D. 0.2 C

Solution

The charge (Q) on a capacitor is given by Q = C * V. Here, Q = 2 x 10^-6 F * 10 V = 20 x 10^-6 C = 20 mC.

Correct Answer: A — 20 mC

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Q. What is the potential difference across a capacitor of 2 µF charged to 10V?

A. 20 µC
B. 10 µC
C. 5 µC
D. 15 µC

Solution

Q = C * V = 2 µF * 10V = 20 µC.

Correct Answer: A — 20 µC

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

A. 0.05 V
B. 0.5 V
C. 5 V
D. 50 V

Solution

V = Q/C; Q = C * V = 5 µF * 10 V = 50 µC, thus the potential difference is 10 V.

Correct Answer: C — 5 V

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

A. 5V
B. 10V
C. 15V
D. 20V

Solution

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

Correct Answer: B — 10V

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Q. What is the potential difference across a capacitor of 5 µF charged to 12 V?

A. 0.06 C
B. 0.06 J
C. 0.06 V
D. 0.06 F

Solution

The energy stored in a capacitor is U = 0.5 * C * V^2 = 0.5 * 5 x 10^-6 F * (12 V)^2 = 0.36 J.

Correct Answer: B — 0.06 J

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Q. What is the potential difference across a capacitor of 5 µF charged with 0.01 C?

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

Solution

V = Q / C = 0.01 C / 5 x 10^-6 F = 2000 V.

Correct Answer: A — 2 V

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Q. What is the potential difference across a capacitor of 8 µF charged with 16 µC?

A. 2V
B. 4V
C. 8V
D. 12V

Solution

Voltage V = Q/C = 16 x 10^-6 C / 8 x 10^-6 F = 2V.

Correct Answer: B — 4V

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Q. What is the potential difference across a capacitor of 8 µF if it stores a charge of 16 µC?

A. 1V
B. 2V
C. 3V
D. 4V

Solution

Using the formula Q = C * V, we have V = Q / C = 16 x 10^-6 C / 8 x 10^-6 F = 2V.

Correct Answer: B — 2V

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Electrostatics & Circuits

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