What is the dimensional formula for electric charge?
Practice Questions
Q1
What is the dimensional formula for electric charge?
[M^1 L^2 T^-3 I^-1]
[M^0 L^0 T^1 I^1]
[M^0 L^1 T^-2 I^1]
[M^1 L^1 T^-2 I^-1]
Questions & Step-by-Step Solutions
What is the dimensional formula for electric charge?
Correct Answer: [M^1 L^2 T^-3 I^-1]
Step 1: Understand that electric charge (Q) is related to electric current (I).
Step 2: Recall the formula for electric current: I = Q/t, where 't' is time.
Step 3: Rearrange the formula to express charge: Q = I * t.
Step 4: Identify the dimensions of each variable: Current (I) has the dimension [I^1], and time (t) has the dimension [T^1].
Step 5: Substitute the dimensions into the equation: Q = [I^1] * [T^1].
Step 6: To find the dimensional formula for charge, we need to express current in terms of mass (M), length (L), and time (T).
Step 7: The dimensional formula for current (I) can be derived from the formula for electric power: P = I^2 * R, where R is resistance with dimensions [M^1 L^2 T^-3 I^-2].
Step 8: Rearranging gives us I = sqrt(P/R), leading to the dimensions of current: [M^1 L^2 T^-3 I^-2]^(1/2) = [M^0.5 L^1 T^-1.5 I^-1].
Step 9: Substitute this back into the charge formula: Q = [M^0.5 L^1 T^-1.5 I^-1] * [T^1].
