Question

The power in an electrical circuit is give by P = At² + Ct, where t is the time. What will be the dimension A and C respectively are 
1. [ML²T^-5] and [ML²T^-4]
2. [ML^-1T^-3] and [ML]
3. [LT^-2] and [LT^-1]
4. [ML³T] and [MLT³]

Answer 1

Correct Answer - Option 1 : [ML²T^-5] and [ML²T^-4]

CONCEPT:

• Measurement of any physical quantity involves comparison with a certain basic, arbitrarily chosen, internationally accepted reference standard called unit, and a Dimension is a mathematical tool used for studying the nature of physical quantities. 
• The basic concept of dimensions is that we can add or subtract only those quantities which have the same dimensions.
• And the dimensional formula is defined as the expression of the physical quantity in terms of mass, length, and time.

CALCULATION:

Given -  The dimension of the power is [ML²T^-3]

The equation is given 

⇒ P = At² + Ct

The dimension of A will be 

At² = Dimension of power

⇒At² = [ML2T-3]

• The dimension of A will be

\(⇒ Dimesion\ of \ A = \frac{ML^{2}T^{-3}}{T^{2}} = ML^{2}T^{-5}\)

• Similarly, the dimension of C will be

\(⇒ Dimension\ of \ C = \frac{[ML^{2}T^{-3}]}{[T]} = [ML^{2}T^{-4}]\)

• Hence, option 1  is the answer