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Static and current electricity

Chapter: Electricity and Magnetism

Question 1 of 5 NDA MCQ

Which of the following statements correctlyexplains/explain the existence of a positive forcebetween two electric charges?

1. Both the charges are positive.

2. Both the charges are negative.

3. Both the charges are oppositely charged.

Select the correct answer using the code givenbelow.

Detailed Explanation

Correct Answer

✓ Option (c) is correct. Both charges being positive or negative results in a repulsive force.

📖 Governing Law / Core Concept

The existence of a force between electric charges is governed by Coulomb's Law, which states:

\[ F = k \frac{|q_1 q_2|}{r^2} \]

Where:

  • F = Force between charges (N)
  • k = Coulomb's constant (\(8.99 \times 10^9 \, \text{N m}^2/\text{C}^2\))
  • q_1, q_2 = Magnitude of charges (C)
  • r = Distance between centers of charges (m)

🧪 Step-by-Step Breakdown

The force between two like charges (both positive or both negative) is repulsive, resulting in:

  • Positive force value (repulsion).

When one charge is positive and the other is negative:

  • Negative force value indicating attraction.

Thus, only options 1 and 2 lead to a positive force.

🔍 Option Analysis

Option 1: Both positive charges result in repulsion.

Option 2: Both negative charges also lead to repulsion.

Option 3: Opposite charges attract, giving a negative force.

⚡ Mnemonic / Speed-Run

Remember: "Like Charges Repel, Unlike Charges Attract" to quickly identify charge interactions.

6. Visual Suggestion

6. Visual Suggestion

A schematic diagram showing two positive charges with arrows indicating repulsion, and two negative charges similarly represented, contrasting with arrows between a positive and a negative charge indicating attraction.

📖 Factual Verification & Reference

📖 Factual Verification & Reference:

Verified against NCERT Class XI Physics, Chapter 2: Electrostatics.

Question 2 of 5 NDA MCQ

If the current through an electrical machine running on direct current is 15 A and the machine runs for 10 minutes, the charge that passes through the machine during this time is:

Detailed Explanation

Solution

Option (d) is correct.

Explanation:

\[ q = i \cdot t \]
Where:
  • \( q \) = Charge (Coulombs)
  • \( i \) = Current (Amperes) = 15 A
  • \( t \) = Time (Seconds) \end{aligned}
Convert time from minutes to seconds:
\[ t = 10 \, \text{minutes} \times 60 \, \text{seconds/minute} = 600 \, \text{seconds} \]
Substituting the values:
\[ q = 15 \, \text{A} \times 600 \, \text{s} = 9000 \, \text{C} \]
📌 Hints / Properties Used:
  • Charge, \( q = i \cdot t \)
  • 1 Ampere = 1 Coulomb/second
📊 Visual Diagram Suggestion:

A circuit diagram with a battery, switch, and resistor showing the direction of current and the flow of charge over time would help visualize the flow of electrons and resulting charge calculations.

📖 Factual Verification & Reference:

Verified against NCERT Class XI Physics, Chapter 6 (Current Electricity).

Question 3 of 5 NDA MCQ

Which one of the following is primarily responsible for conduction of current in a metal?

Detailed Explanation

Correct Answer

✓ Option B is correct. Free electrons are primarily responsible for the conduction of current in metals.

📖 Governing Law / Core Concept

Electrical conductivity in metals is governed by the principle of free electron theory. In conductive materials, free electrons facilitate the transfer of electric charge.

🧪 Step-by-Step Breakdown

In a metal, the electrons are categorized as bound (not moving) and free (mobile).

1. Free electrons are weakly bound to the metal lattice due to the low ionization energy of metals.

2. The electric current \( I \) can be represented as:

\[ I = n \cdot A \cdot e \cdot v_d \]

Where:

  • \( n \) = number density of free electrons (m−3)
  • \( A \) = cross-sectional area of wire (m2)
  • \( e \) = charge of an electron (Coulombs, C)
  • \( v_d \) = drift velocity of electrons (m/s)

The drift velocity reflects how free electrons move in response to an electric field.

🔍 Option Analysis

Option A (Bound electrons) do not contribute effectively to conductivity as they are not free to move. Option C (Both bound and free electrons) is incorrect as bound electrons cannot conduct current. Option D (Ions) also contribute negligibly compared to free electrons.

⚡ Mnemonic / Speed-Run

Mneuonic: "Free to Flow" - only free electrons circulate to maintain electrical flow.

6. Visual Suggestion

6. Visual Suggestion

A schematic diagram showing a metal conductor with free electrons highlighted in motion, indicating their movement as current flows through the conductor.

📖 Factual Verification & Reference

📖 Factual Verification & Reference:

Verified against NCERT Class XII Physics, Chapter 3 (Current Electricity).

Question 4 of 5 NDA MCQ

The AC mains domestic supply current in India changes direction in every:

Detailed Explanation

Correct Answer

✓ Option (d) is correct. AC current changes direction every 1/100 seconds.

📖 Governing Law / Core Concept

In alternating current (AC) systems, the frequency of the AC supply determines the time taken for the current to change direction. The formula for frequency (\( f \)) is given by:

\[ f = \frac{1}{T} \]

Where \( T \) is the time period in seconds. In India, the frequency of AC is 50 Hz.

🧪 Step-by-Step Breakdown

To calculate the time period \( T \) of the AC supply:

\[ T = \frac{1}{f} = \frac{1}{50} = 0.02 \text{ s} \]

The AC current inverts its direction once during each half-cycle. Therefore, the time for a complete direction change is:

\[ T_{change} = \frac{T}{2} = \frac{0.02}{2} = 0.01 \text{ s} = \frac{1}{100} \text{ s} \]

🔍 Option Analysis

  • Option (a): 50 s - Incorrect; far too long for practical AC usage.
  • Option (b): 1/50 s - Incorrect; this would correspond to a higher frequency than typical AC.
  • Option (c): 100 s - Incorrect; outside the range of domestic supply.
  • Option (d): 1/100 s - Correct; matches the AC frequency in India.

⚡ Mnemonic / Speed-Run

Remember: For AC systems, frequency and time period are inversely related. 50 Hz translates to a direction change of 1/100 seconds.

6. Visual Suggestion

Include a cycle diagram illustrating the AC waveform, highlighting the direction change points every 1/100 seconds.

📖 Factual Verification & Reference

📖 Factual Verification & Reference:

Verified against NCERT Class 12 Physics, Chapter on Alternating Current.

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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