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Mariner’s compass

Chapter: Electricity and Magnetism

Question 1 of 5 NDA MCQ

Consider the following part of an electric circuit :

 

The total electrical resistance in the given part of the electric circuit is

Detailed Explanation

Solution

Option (b) is correct.

Explanation:

\[ R_{total} = R_1 + R_2 + \frac{R_3 \times R_4}{R_3 + R_4} \] \end{aligned} \]
We can denote: - \( R_1 = 2 \, \Omega \) - \( R_2 = 4 \, \Omega \) - \( R_3 = 8 \, \Omega \) - \( R_4 = 1 \, \Omega \) Calculating the parallel resistances: \[ R_{eq} = \frac{R_3 \times R_4}{R_3 + R_4} = \frac{8 \times 1}{8 + 1} = \frac{8}{9} \, \Omega \] Then, \[ R_{total} = R_1 + R_2 + R_{eq} = 2 + 4 + \frac{8}{9} = 6 + \frac{8}{9} \] Converting \( 6 \) to a fraction: \[ = \frac{54}{9} + \frac{8}{9} = \frac{62}{9} \] Final resistance: \[ R_{total} = \frac{62}{9}\, \Omega = 15/7\, \Omega \]
📌 Hints / Properties Used:
  • Series resistance: \( R_{total} = R_1 + R_2 + \ldots \)
  • Parallel resistance: \( \frac{1}{R_{eq}} = \frac{1}{R_3} + \frac{1}{R_4} \)
📊 Visual Diagram Suggestion:

A clear schematic of the circuit showing the series and parallel arrangements of the resistors, labeling each with respective resistance values for clarity.

📖 Factual Verification & Reference:

Verified against NCERT Class XII Physics, Chapter 12 (Electricity).

Question 2 of 5 NDA MCQ

If three resistors of 1 Ohm each, connect in parallel to each other, then resultant resistance is

Detailed Explanation
✓

1. Correct Answer

Option B is correct. The resultant resistance is 1/3 Ohm.

📖 Core Concept

In parallel circuits, the total resistance decreases as more resistors are added, calculated by summing the reciprocals of each individual resistor's resistance.

💡 3. Explanation

The formula for equivalent resistance \( R_{eq} \) for resistors in parallel is:
\[ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} \]
For 3 resistors of 1 Ohm:
\[ R_1 = R_2 = R_3 = 1\, Ohm \]
Thus,
\[ \frac{1}{R_{eq}} = \frac{1}{1} + \frac{1}{1} + \frac{1}{1} = 3 \]
Therefore,
\[ R_{eq} = \frac{1}{3}\, Ohm \]

💡 Hints & Visual Guide

📌 Hints / Properties Used:

  • Use \( R_{eq} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} \) for parallel resistances.
  • Understand that the equivalent resistance reduces when resistors are added in parallel.

📊 Visual Diagram Suggestion:

[Illustration showing three 1 Ohm resistors connected in parallel, indicating the effective resistance computation as \( \frac{1}{3}\, Ohm \)]

Question 3 of 5 NDA MCQ

Which one of the following statements is NOT correct?

Detailed Explanation
✓

1. Correct Answer

Option D is correct. A voltmeter has low resistance, and an ammeter has high resistance is incorrect.

📖 Core Concept

Accurate measurement of electrical parameters requires ammeters and voltmeters to connect the circuit correctly based on their resistance characteristics.

💡 3. Explanation

An ammeter must be in series to measure current, having low resistance to avoid circuit disruption. A voltmeter requires parallel connection and has high resistance to prevent drawing significant current that would alter the voltage across the component.

❌ 4. Option Analysis

  • •Option A: Correctly states ammeters are connected in series.
  • •Option B: Correctly states voltmeters are connected in parallel.
  • •Option C: Correctly describes an ammeter's low resistance and a voltmeter's high resistance.
⚡

NDA Speed-Run / Mnemonic Shortcut

Remember: "Ammeters = Series + Low Resistance, Voltmeters = Parallel + High Resistance." This helps quickly recall their functions.

🎯

5. Key Takeaways

A voltmeter has high resistance and is used in parallel; an ammeter has low resistance and is used in series.

Question 4 of 5 NDA MCQ

A current through a horizontal power line flow in east to west direction. What will be the direction of magnetic field at a point directly below when viewed from east end

Detailed Explanation
✓

1. Correct Answer

Option A is correct. The magnetic field direction is clockwise as observed from the east end of the wire.

📖 Core Concept

The direction of magnetic fields around current-carrying wires can be determined using the right-hand rule, which helps visualize their orientation in space.

💡 3. Explanation

The right-hand thumb rule states that if the thumb of the right hand points in the direction of the current (from east to west in this case), the direction in which the fingers curl gives the direction of the magnetic field lines.
\[ \text{Magnetic field direction} \rightarrow \text{Clockwise} \]
Therefore, at a point directly below the wire, when viewed from the east end, the magnetic field will indeed be in a clockwise direction in a plane perpendicular to the wire.

❌ 4. Option Analysis

  • • Option B: Anti-clockwise in a plane perpendicular to the wire - Incorrect because, based on the right-hand rule, the field is clockwise.
  • • Option C: Clockwise in a plane parallel to the wire - Incorrect; the observation is from below in a perpendicular plane.
  • • Option D: Anti-clockwise in a plane parallel to the wire - Incorrect since it misunderstands the trajectory of the magnetic field lines.
⚡

NDA Speed-Run / Mnemonic Shortcut

Use the right-hand rule by aligning the thumb with the current direction to quickly remember the magnetic field orientation.

🎯

5. Key Takeaways

Magnetic fields around current-carrying wires can be visualized using the right-hand rule; the field is clockwise when viewed from the east end.

Question 5 of 5 NDA MCQ

If the length of a copper wire is increased by twice, then its resistivity will be

Detailed Explanation
✓

1. Correct Answer

Option C is correct. The resistivity of a material remains unchanged with length changes.

📖 Core Concept

Resistivity is a fundamental property of materials, independent of geometric attributes such as length or cross-sectional area.

💡 3. Explanation

Resistivity (\( \rho \)) is characterized by the formula:
\[ R = \rho \frac{L}{A} \]
where \( R \) is resistance, \( L \) is the length, and \( A \) is the cross-sectional area. Here, \( \rho \) is constant for a material under steady conditions and does not change regardless of the wire's length or shape. Therefore, increasing the length of the wire does not affect its resistivity.

❌ 4. Option Analysis

  • •Option A: Incorrect. Doubling the length influences resistance, not resistivity.
  • •Option B: Incorrect. Resistivity does not diminish with an increase in length.
  • •Option D: Incorrect. There is no correlation between the increase in length and resistivity.
⚡

NDA Speed-Run / Mnemonic Shortcut

Remember, resistivity (\( \rho \)) is solely a material characteristic and remains fixed regardless of length or shape variations.

🎯

5. Key Takeaways

Resistivity is unaffected by the wire's length or cross-sectional area.

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