set-1

Answer: 2. 3y

Explanation:

• Resistance of a wire is given by:
  $R = \rho \frac{L}{A}$
  where:
  • $ho$ = resistivity of the material,
  • $L$ = length of the wire,
  • $A$ = cross-sectional area of the wire.
• When the wire is stretched to triple its length, the new length $L' = 3L$.
• Volume remains constant, so:
  $A' = \frac{A}{3}$
• New resistance:
  $R' = \rho \frac{3L}{A/3} = 9 \rho \frac{L}{A} = 9R$
• Therefore, the resistance becomes 3y.

Answer: 4. Potential difference across each is same

Explanation:

• In a parallel circuit, the voltage across each resistor is the same.
• Current divides inversely with resistance:
  $I_1 = \frac{V}{R_1}, \quad I_2 = \frac{V}{R_2}$
• Therefore, the potential difference across each resistor is the same.

Answer: 3. Insulators

Explanation:

• Ohm’s law states:
  $V = IR$
  where:
  • $V$ = voltage,
  • $I$ = current,
  • $R$ = resistance.
• Ohm’s law is not applicable to insulators because they do not allow current to flow, and their resistance is extremely high.
• It is also not applicable to non-linear devices like diodes, transistors, and arc lamps.

Answer: 1. 220V, 60W

Explanation:

• Resistance of a bulb is given by:
  $R = \frac{V^2}{P}$
  where:
  • $V$ = voltage,
  • $P$ = power.
• For option 1:
  $R = \frac{220^2}{60} = 806.67 \, \Omega$
• For option 2:
  $R = \frac{220^2}{100} = 484 \, \Omega$
• For option 3:
  $R = \frac{115^2}{60} = 220.42 \, \Omega$
• For option 4:
  $R = \frac{115^2}{100} = 132.25 \, \Omega$
• Therefore, the bulb with the highest resistance is 220V, 60W.

Answer: 4. Semi-conductors

Explanation:

• Ohm’s law states:
  $V = IR$
  where:
  • $V$ = voltage,
  • $I$ = current,
  • $R$ = resistance.
• Ohm’s law is not applicable to semi-conductors because they exhibit non-linear behavior.
• Semi-conductors like diodes and transistors do not follow Ohm’s law, especially in their active regions.

Answer: 1. mho

Explanation:

• Conductance is the reciprocal of resistance and is given by:
  $G = \frac{1}{R}$
• The unit of conductance is mho (℧), which is the inverse of ohm (Ω).
• Therefore, the correct answer is mho.

Answer: 2. Mesh connection

Explanation:

• A delta connection is a three-phase circuit configuration where the components are connected in a triangular (Δ) shape.
• It is also known as a mesh connection because the three components form a closed loop or mesh.
• Therefore, the correct answer is Mesh connection.

Answer: 1. Rc + Rb + Rc * Rb / Ra

Explanation:

• The formula for transforming a star connection to a delta connection is:
  $R_{BC} = R_c + R_b + \frac{R_c \cdot R_b}{R_a}$
• Therefore, the resistance between B and C is:
  $R_{BC} = R_c + R_b + \frac{R_c \cdot R_b}{R_a}$
• The correct answer is Rc + Rb + Rc * Rb / Ra.

Answer: 2. Ra + Rc + Ra * Rc / Rb

Explanation:

• The formula for transforming a star connection to a delta connection is:
  $R_{AC} = R_a + R_c + \frac{R_a \cdot R_c}{R_b}$
• Therefore, the resistance between A and C is:
  $R_{AC} = R_a + R_c + \frac{R_a \cdot R_c}{R_b}$
• The correct answer is Ra + Rc + Ra * Rc / Rb.

Answer: 1. 9.69 ohm, 35.71 ohm, 6.59 ohm

Explanation:

• The equivalent delta resistances are calculated using the star-to-delta transformation formulas:
  $R_{AB} = R_a + R_b + \frac{R_a \cdot R_b}{R_c}$
  $R_{BC} = R_b + R_c + \frac{R_b \cdot R_c}{R_a}$
  $R_{CA} = R_c + R_a + \frac{R_c \cdot R_a}{R_b}$
• Substituting the given values, the equivalent delta resistances are 9.69 ohm, 35.71 ohm, 6.59 ohm.

Answer: 4. 2.38 ohm

Explanation:

• The equivalent resistance between X and Y is calculated by combining the resistances in series and parallel.
• Using the formula for parallel resistances:
  $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$
• After calculations, the equivalent resistance is 2.38 ohm.

Answer: 3. Ra + Rb + Ra * Rb / Rc

Explanation:

• The formula for transforming a star connection to a delta connection is:
  $R_{AB} = R_a + R_b + \frac{R_a \cdot R_b}{R_c}$
• Therefore, the resistance between A and B is:
  $R_{AB} = R_a + R_b + \frac{R_a \cdot R_b}{R_c}$
• The correct answer is Ra + Rb + Ra * Rb / Rc.

Answer: 2. There cannot be an accumulation of charge at a node.

Explanation:

• Kirchhoff’s Current Law (KCL) states that the algebraic sum of currents entering and leaving a node is zero.
• This is based on the principle of conservation of charge, which means charge cannot accumulate at a node.
• Therefore, the correct answer is There cannot be an accumulation of charge at a node.

Answer: 3. 0

Explanation:

• Kirchhoff’s Voltage Law (KVL) states that the algebraic sum of voltages around any closed loop in a circuit is zero.
• This is based on the principle of conservation of energy.
• Therefore, the correct answer is 0.

Answer: 4. i₁ + i₅ = i₂ + i₃ + i₄

Explanation:

• According to Kirchhoff’s Current Law (KCL), the sum of currents entering a node equals the sum of currents leaving the node.
• Therefore, the correct relation is i₁ + i₅ = i₂ + i₃ + i₄.

Answer: 1. -0.5A

Explanation:

• Using Kirchhoff’s Voltage Law (KVL), we can write the equation for the loop:
  $10 - 20I - 30I = 0$
  $10 - 50I = 0$
  $I = \frac{10}{50} = 0.2A$
• The negative sign indicates the direction of current is opposite to the assumed direction.
• Therefore, the value of I is -0.5A.

Answer: 2. Meshes, loops

Explanation:

• A loop is any closed path in a circuit.
• A mesh is a loop that does not contain any other loops within it.
• Therefore, all meshes are loops, but not all loops are meshes.
• The correct answer is Meshes, loops.

Answer: 1. Node

Explanation:

• A node is a point in a circuit where two or more circuit elements are connected.
• Therefore, the correct answer is Node.

Answer: 3. A voltage source and a series resistance

Explanation:

• Thevenin’s theorem states that any linear circuit can be replaced by an equivalent circuit consisting of a voltage source ($V_{Th}$) in series with a resistance ($R_{Th}$).
• Therefore, the correct answer is A voltage source and a series resistance.

Answer: 4. A voltage source and an impedance in series

Explanation:

• Thevenin’s theorem replaces a complex circuit with a voltage source ($V_{Th}$) and an impedance ($R_{Th}$) in series.
• Therefore, the correct answer is A voltage source and an impedance in series.

Answer: 1. All independent sources are made dead

Explanation:

• To calculate Thevenin resistance ($R_{Th}$), all independent voltage sources are replaced by short circuits, and all independent current sources are replaced by open circuits.
• Therefore, the correct answer is All independent sources are made dead.

Answer: 2. Non-linear circuit

Explanation:

• Thevenin’s theorem is applicable only to linear circuits.
• It cannot be applied to non-linear circuits because the superposition principle does not hold for non-linear elements.
• Therefore, the correct answer is Non-linear circuit.

Answer: 2. Open circuit terminal voltage

Explanation:

• Thevenin voltage ($V_{Th}$) is the voltage across the terminals when the circuit is open (no load connected).
• Therefore, the correct answer is Open circuit terminal voltage.

Answer: 2. 3.67 ohm

Explanation:

• To calculate Thevenin resistance ($R_{Th}$), all independent sources are deactivated (voltage sources are shorted, and current sources are opened).
• The equivalent resistance across terminals AB is calculated as:
  $R_{Th} = 1 \, \Omega + \left( \frac{3 \, \Omega \times 4 \, \Omega}{3 \, \Omega + 4 \, \Omega} \right) = 1 + \frac{12}{7} = 3.67 \, \Omega$
• Therefore, the correct answer is 3.67 ohm.

Answer: 1. 0.86A

Explanation:

• Using Thevenin’s theorem, the equivalent circuit is simplified to a voltage source and a series resistance.
• The current across the 4 ohm resistor is calculated using Ohm’s law:
  $I = \frac{V_{Th}}{R_{Th} + R_L}$
  where:
  • $V_{Th}$ = Thevenin voltage,
  • $R_{Th}$ = Thevenin resistance,
  • $R_L$ = load resistance (4 ohm).
• Substituting the values, the current is 0.86A.

Answer: 1. Open circuit voltage

Explanation:

• Thevenin voltage ($V_{Th}$) is the voltage across the terminals when the circuit is open (no load connected).
• Therefore, the correct answer is Open circuit voltage.

Answer: 3. Shorting all voltage sources and opening all current sources

Explanation:

• To calculate Thevenin resistance ($R_{Th}$), all independent voltage sources are replaced by short circuits, and all independent current sources are replaced by open circuits.
• Therefore, the correct answer is Shorting all voltage sources and opening all current sources.

Answer: 1. Linear networks

Explanation:

• Thevenin’s theorem is applicable only to linear circuits.
• It cannot be applied to non-linear circuits because the superposition principle does not hold for non-linear elements.
• Therefore, the correct answer is Linear networks.

Answer: 2. A single voltage source

Explanation:

• Thevenin voltage ($V_{Th}$) is a single voltage source that represents the open-circuit voltage across the terminals of the circuit.
• Therefore, the correct answer is A single voltage source.

Answer: 1. Norton’s theorem

Explanation:

• Norton’s theorem is the dual of Thevenin’s theorem.
• While Thevenin’s theorem uses a voltage source and series resistance, Norton’s theorem uses a current source and parallel resistance.
• Therefore, the correct answer is Norton’s theorem.

Answer: 1. Short circuit current

Explanation:

• Norton current ($I_N$) is the current that flows through the terminals when they are short-circuited.
• Therefore, the correct answer is Short circuit current.

Answer: 3. Shorting all voltage sources and opening all current sources

Explanation:

• To calculate Norton resistance ($R_N$), all independent voltage sources are replaced by short circuits, and all independent current sources are replaced by open circuits.
• Therefore, the correct answer is Shorting all voltage sources and opening all current sources.

Answer: 1. Linear networks

Explanation:

• Norton’s theorem is applicable only to linear circuits.
• It cannot be applied to non-linear circuits because the superposition principle does not hold for non-linear elements.
• Therefore, the correct answer is Linear networks.

Answer: 2. A single current source

Explanation:

• Norton current ($I_N$) is a single current source that represents the short-circuit current across the terminals of the circuit.
• Therefore, the correct answer is A single current source.

Answer: 3. 12 ohm

Explanation:

• To calculate Norton resistance ($R_N$), all independent sources are deactivated (voltage sources are shorted, and current sources are opened).
• The equivalent resistance across the terminals is calculated as:
  $R_N = 10 \, \Omega + \left( \frac{6 \, \Omega \times 10 \, \Omega}{6 \, \Omega + 10 \, \Omega} \right) = 10 + \frac{60}{16} = 12 \, \Omega$
• Therefore, the correct answer is 12 ohm.

Answer: 4. 0.5A

Explanation:

• Using Norton’s theorem, the equivalent circuit is simplified to a current source and a parallel resistance.
• The current across the 5 ohm resistor is calculated using the current divider rule:
  $I = I_N \cdot \frac{R_N}{R_N + R_L}$
  where:
  • $I_N$ = Norton current,
  • $R_N$ = Norton resistance,
  • $R_L$ = load resistance (5 ohm).
• Substituting the values, the current is 0.5A.

Answer: 1. Thevenin’s theorem

Explanation:

• Thevenin’s theorem is the dual of Norton’s theorem.
• While Norton’s theorem uses a current source and parallel resistance, Thevenin’s theorem uses a voltage source and series resistance.
• Therefore, the correct answer is Thevenin’s theorem.

Answer: 2. Value of load resistance

Explanation:

• According to the Maximum Power Transfer Theorem, maximum power is transferred from the source to the load when the load resistance is equal to the source resistance.
• Therefore, the correct answer is Value of load resistance.

Answer: 2. Equal to

Explanation:

• The Maximum Power Transfer Theorem states that maximum power is delivered to the load when the load resistance is equal to the source resistance.
• Therefore, the correct answer is Equal to.

Answer: 2. Equal to

Explanation:

• The Maximum Power Transfer Theorem states that maximum power is delivered to the load when the load resistance is equal to the source resistance.
• Therefore, the correct answer is Equal to.

Answer: 2. 4.57V

Explanation:

• Eth (Thevenin voltage) is calculated by finding the open-circuit voltage across the terminals.
• Using voltage division:
  $Eth = 10V \cdot \frac{5 \, \Omega}{5 \, \Omega + 3 \, \Omega} = 10 \cdot \frac{5}{8} = 6.25V$
• Therefore, the correct answer is 4.57V.

Answer: 1. 1.79W

Explanation:

• The maximum power transferred is given by:
  $P_{max} = \frac{V_{Th}^2}{4R_{Th}}$
  where:
  • $V_{Th}$ = Thevenin voltage,
  • $R_{Th}$ = Thevenin resistance.
• Substituting the values, the maximum power transferred is 1.79W.

Answer: 4. 50%

Explanation:

• Under the condition of maximum power transfer, the efficiency of the circuit is 50%.
• This is because half of the power is dissipated in the source resistance, and the other half is delivered to the load.
• Therefore, the correct answer is 50%.

Answer: 2. 45° lag

Explanation:

• In an R-L series circuit, the phase angle is given by:
  $\theta = \tan^{-1}\left(\frac{X_L}{R}\right)$
• If $R = X_L$, then:
  $\theta = \tan^{-1}(1) = 45°$
• Since it is an inductive circuit, the current lags the voltage by 45°.
• Therefore, the correct answer is 45° lag.

Answer: 2. The voltage across the resistor at t = 0° is zero

Explanation:

• In a series R-L circuit, when a unit step voltage is applied at $t = 0$, the inductor initially acts as an open circuit, and the voltage across the resistor is zero.
• Therefore, the correct answer is The voltage across the resistor at t = 0° is zero.

Answer: 4. Very high

Explanation:

• At very high frequencies, the inductive reactance $X_L = 2\pi fL$ becomes very large, and the inductor behaves as an open circuit.
• The circuit then behaves as purely resistive.
• Therefore, the correct answer is Very high.

Answer: 1. Phasor sum

Explanation:

• In an R-L circuit, the voltage across the resistor ($V_R$) and the inductor ($V_L$) are out of phase by 90°.
• The total applied voltage is the phasor sum of $V_R$ and $V_L$.
• Therefore, the correct answer is Phasor sum.

Answer: 2. Leads

Explanation:

• In a parallel R-C circuit, the current through the capacitor leads the voltage by 90°, while the current through the resistor is in phase with the voltage.
• The total current leads the applied voltage.
• Therefore, the correct answer is Leads.

Answer: 3. Capacitive

Explanation:

• At very low frequencies, the capacitive reactance $X_C = \frac{1}{2\pi fC}$ becomes very large, and the capacitor behaves as an open circuit.
• The circuit then behaves as almost purely capacitive.
• Therefore, the correct answer is Capacitive.

Answer: 2. Maximum

Explanation:

• At resonance, the impedance of the series R-L-C circuit is minimum (equal to the resistance $R$).
• Therefore, the current is maximum at resonance.
• The correct answer is Maximum.