What is the dimensional formula for electric charge?

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Q: What is the dimensional formula for electric charge?

Solution: The dimensional formula for electric charge is [M^1 L^2 T^-3 I^-1], derived from the definition of current (I = Q/t).

Steps: 12

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].
Step 10: Combine the dimensions: Q = [M^0.5 L^1 T^(-1.5 + 1) I^-1] = [M^0.5 L^1 T^-0.5 I^-1].
Step 11: To express in standard form, we can multiply by T^3/T^3 to get: Q = [M^1 L^2 T^-3 I^-1].
Step 12: Therefore, the final dimensional formula for electric charge is [M^1 L^2 T^-3 I^-1].