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. A capacitor is charged to a voltage of 15 V and then disconnected from the battery. If the capacitance is 3 µF, what is the charge on the capacitor?

A. 45 µC
B. 30 µC
C. 15 µC
D. 60 µC

Solution

Charge (Q) is given by Q = CV. Here, Q = 3 µF * 15 V = 45 µC.

Correct Answer: A — 45 µC

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Q. A capacitor is charged to a voltage of 15 V and then disconnected from the power supply. What happens to the charge on the capacitor if the voltage is doubled?

A. Charge doubles
B. Charge halves
C. Charge remains the same
D. Charge becomes zero

Solution

If the voltage is doubled, the charge on the capacitor also doubles, since Q = C * V.

Correct Answer: A — Charge doubles

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

A. 0.125 mJ
B. 0.25 mJ
C. 0.5 mJ
D. 1 mJ

Solution

Energy stored, U = 0.5 * C * V² = 0.5 * 10 x 10^-6 F * (5 V)² = 0.125 mJ.

Correct Answer: B — 0.25 mJ

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Q. A capacitor with a capacitance of 10μF is charged to a voltage of 5V. What is the charge stored in the capacitor?

A. 10μC
B. 50μC
C. 5μC
D. 100μC

Solution

The charge stored in a capacitor is given by Q = C * V = 10μF * 5V = 50μC.

Correct Answer: B — 50μC

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Q. A circuit has a total voltage of 12V and a total resistance of 3 ohms. What is the total current in the circuit?

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

Solution

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

Correct Answer: A — 4 A

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Q. According to Coulomb's law, what is the force between two charges of +3 µC and -2 µC separated by a distance of 0.1 m?

A. 0.54 N
B. 0.60 N
C. 0.72 N
D. 0.80 N

Solution

Force F = k * |q₁ * q₂| / r² = (8.99 x 10^9 N m²/C² * |3 x 10^-6 C * -2 x 10^-6 C|) / (0.1 m)² = 0.54 N.

Correct Answer: A — 0.54 N

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Q. According to Kirchhoff's Voltage Law, the sum of the voltages around a closed loop is equal to what?

A. Zero
B. The total current
C. The total resistance
D. The total power

Solution

Kirchhoff's Voltage Law states that the sum of the voltages around a closed loop is equal to zero.

Correct Answer: A — Zero

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Q. During the transient response of an RC circuit, what is the behavior of the voltage across the capacitor?

A. It increases linearly
B. It decreases exponentially
C. It increases exponentially
D. It remains constant

Solution

During the transient response of an RC circuit, the voltage across the capacitor increases exponentially until it reaches the supply voltage.

Correct Answer: C — It increases exponentially

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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

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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

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Q. If a capacitor discharges through a resistor, what is the formula for the voltage across the capacitor at time t?

A. V(t) = V0 * e^(-t/RC)
B. V(t) = V0 * (1 - e^(-t/RC))
C. V(t) = V0 * t/RC
D. V(t) = V0 * e^(t/RC)

Solution

The voltage across a discharging capacitor is given by V(t) = V0 * e^(-t/RC).

Correct Answer: A — V(t) = V0 * e^(-t/RC)

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Q. If a capacitor discharges through a resistor, what is the voltage across the capacitor after one time constant?

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

Solution

After one time constant (τ), the voltage across the capacitor will be V0/e, where V0 is the initial voltage.

Correct Answer: A — V0/e

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Q. If a capacitor has a capacitance of 10μF and is charged to a voltage of 5V, what is the charge stored in the capacitor?

A. 50μC
B. 5μC
C. 10μC
D. 100μC

Solution

The charge stored in a capacitor is given by Q = C * V = 10μF * 5V = 50μC.

Correct Answer: A — 50μC

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Q. If a capacitor has a capacitance of 2μF and is charged to 10V, what is the charge stored in the capacitor?

A. 20μC
B. 5μC
C. 2μC
D. 10μC

Solution

The charge stored in the capacitor is given by Q = C*V = 2μF * 10V = 20μC.

Correct Answer: A — 20μC

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Q. If a capacitor has a capacitance of 5μF and is charged to a voltage of 10V, what is the charge stored in the capacitor?

A. 0.05C
B. 0.1C
C. 0.5C
D. 1C

Solution

Charge (Q) is given by Q = C * V = 5μF * 10V = 0.05C.

Correct Answer: A — 0.05C

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Q. If a capacitor is charged to a voltage of 20 V and then connected in parallel with another uncharged capacitor of the same capacitance, what is the new voltage across both capacitors?

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

Solution

When two identical capacitors are connected in parallel, the charge is shared equally. The new voltage is halved: 20 V / 2 = 10 V.

Correct Answer: A — 10 V

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Q. If a capacitor is charged to a voltage V and then disconnected from the power source, what happens to the charge on the capacitor over time?

A. It remains constant
B. It decreases exponentially
C. It increases exponentially
D. It becomes zero instantly

Solution

When a capacitor is disconnected from the power source, the charge decreases exponentially over time due to leakage.

Correct Answer: B — It decreases exponentially

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Q. If a capacitor is connected to an AC source, what happens to the current through the capacitor?

A. It is constant
B. It leads the voltage
C. It lags the voltage
D. It is zero

Solution

In an AC circuit, the current through a capacitor leads the voltage by 90 degrees.

Correct Answer: B — It leads the voltage

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

A. 0.02 J
B. 0.1 J
C. 0.5 J
D. 0.1 mJ

Solution

Energy stored, U = 0.5 * C * V^2 = 0.5 * 10 x 10^-6 F * (20 V)^2 = 0.02 J.

Correct Answer: B — 0.1 J

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Q. If a capacitor of 10 µF is charged to a voltage of 5V, what is the stored energy?

A. 0.125 mJ
B. 0.25 mJ
C. 0.5 mJ
D. 0.75 mJ

Solution

Energy stored U = 0.5 * C * V^2 = 0.5 * 10 x 10^-6 F * (5V)^2 = 0.125 mJ.

Correct Answer: B — 0.25 mJ

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Q. If a capacitor of 10 µF is connected in series with a 20 µF capacitor, what is the total capacitance?

A. 6.67 µF
B. 30 µF
C. 15 µF
D. 8 µF

Solution

1/C_total = 1/C1 + 1/C2 = 1/10 + 1/20 = 3/20, thus C_total = 20/3 µF = 6.67 µF.

Correct Answer: A — 6.67 µF

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Q. If a capacitor of 5 microfarads is charged to 20 volts, what is the energy stored in the capacitor?

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

Solution

The energy (U) stored in a capacitor is given by U = 0.5 * C * V^2. Here, U = 0.5 * 5 x 10^-6 F * (20^2) = 0.02 J.

Correct Answer: B — 0.02 J

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

A. 0.36 mJ
B. 0.72 mJ
C. 1.44 mJ
D. 2.88 mJ

Solution

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

Correct Answer: A — 0.36 mJ

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Q. If a capacitor of 5 µF is charged to a voltage of 10 V, what is the charge stored in the capacitor?

A. 50 µC
B. 100 µC
C. 25 µC
D. 75 µC

Solution

Charge (Q) = C * V = 5 µF * 10 V = 50 µC.

Correct Answer: A — 50 µC

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

A. 0.25 mJ
B. 0.5 mJ
C. 0.75 mJ
D. 1.0 mJ

Solution

Energy stored, 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. If a capacitor of 5 µF is charged to a voltage of 10V, what is the stored energy?

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

Solution

Energy stored, 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. If a circuit has a total current of 5 A and a total resistance of 10 Ω, what is the total voltage?

A. 50 V
B. 25 V
C. 10 V
D. 5 V

Solution

Using Ohm's Law, V = I * R = 5 A * 10 Ω = 50 V.

Correct Answer: A — 50 V

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Q. If a circuit has a total resistance of 10 Ω and a current of 2 A, what is the voltage across the circuit?

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

Solution

Using Ohm's Law: V = I * R = 2 A * 10 Ω = 20 V.

Correct Answer: C — 20 V

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Q. If a circuit has a total resistance of 10Ω and a current of 5A, what is the voltage across the circuit?

A. 10V
B. 15V
C. 50V
D. 5V

Solution

Using Ohm's Law, V = I * R = 5A * 10Ω = 50V.

Correct Answer: C — 50V

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Q. If a circuit has a total resistance of 10Ω and a total current of 2A, what is the total voltage supplied by the battery?

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

Solution

Using Ohm's Law, V = I * R = 2A * 10Ω = 20V.

Correct Answer: B — 10V

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Electrostatics & Circuits

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