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Which of the following is the correct dimensional formula for electric charge?

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Question: Which of the following is the correct dimensional formula for electric charge?

Options:

  1. [M^1 L^2 T^-3 A^-1]
  2. [M^0 L^0 T^0 A^1]
  3. [M^0 L^1 T^-2 A^1]
  4. [M^1 L^1 T^-2 A^-1]

Correct Answer: [M^1 L^2 T^-3 A^-1]

Solution:

The dimensional formula for electric charge is [M^1 L^2 T^-3 A^-1], derived from the definition of current.

Which of the following is the correct dimensional formula for electric charge?

Practice Questions

Q1
Which of the following is the correct dimensional formula for electric charge?
  1. [M^1 L^2 T^-3 A^-1]
  2. [M^0 L^0 T^0 A^1]
  3. [M^0 L^1 T^-2 A^1]
  4. [M^1 L^1 T^-2 A^-1]

Questions & Step-by-Step Solutions

Which of the following is the correct dimensional formula for electric charge?
  • Step 1: Understand that electric charge is related to electric current.
  • Step 2: Recall the definition of electric current (I), which is the flow of electric charge (Q) per unit time (t). The formula is I = Q/t.
  • Step 3: Rearrange the formula to express electric charge: Q = I * t.
  • Step 4: Identify the dimensions of each component: Current (I) has the dimensional formula [A] (Ampere), and time (t) has the dimensional formula [T] (seconds).
  • Step 5: Substitute the dimensions into the equation: Q = [A] * [T].
  • Step 6: This gives us the dimensional formula for charge as [A T].
  • Step 7: Now, we need to express current (I) in terms of base dimensions: Current (I) can be expressed as [M^1 L^2 T^-3 A^-1] based on the relationship with other physical quantities.
  • Step 8: Therefore, the dimensional formula for electric charge (Q) becomes [M^1 L^2 T^-3 A^-1].
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