Question: The magnetic flux $\phi$ (in Wb) linked with a coil is related to time $t$ (in s) as $\phi = 5At^2 + Bt - 2C$. The SI units of A and B are respectively:

Step 1 (Principle of Homogeneity of Dimensions): [0.25 Mark]
According to the Principle of Homogeneity of Dimensions, terms added or subtracted in an equation must have the same physical dimensions. Since $\phi$ is measured in Weber (Wb), each term on the right-hand side must also have the unit of Weber (Wb).

Step 2 (Step-by-Step Mathematical Working): [0.5 Mark]
Given the equation: $\phi = 5At^2 + Bt - 2C$

• For the first term: $[5At^2] = [\phi]$
  Units of $A \times (\text{s})^2 = \text{Wb}$
  Units of $A = \frac{\text{Wb}}{\text{s}^2} = \text{Wb s}^{-2}$
• For the second term: $[Bt] = [\phi]$
  Units of $B \times (\text{s}) = \text{Wb}$
  Units of $B = \frac{\text{Wb}}{\text{s}} = \text{Wb s}^{-1}$

Step 3 (Final Concluded Answer): [0.25 Mark]
Comparing the derived units with the given options, we find that the SI units of $A$ and $B$ are $\text{Wb s}^{-2}$ and $\text{Wb s}^{-1}$ respectively.
Correct Option: (C) $\text{Wb s}^{-2}$, $\text{Wb s}^{-1}$

💡 EL10 Concept Insight: Think of this like adding apples to apples; if the total result is in "Webers," then every individual part of the equation must also be in "Webers." By dividing the total unit (Wb) by the time units ($t^2$ or $t$), we simply find out what the constants $A$ and $B$ need to be to make the math balance out perfectly.