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