NTA Abhyas 2020
- Exam
- NTA Abhyas
- Year
- 2020
- Subject
- Physics
- Chapter
- Units and Dimensions
NTA Abhyas 2020 · Physics · Units and Dimensions
If C, R, LandI denote capacity, resistance, inductance and electric...
If denote capacity, resistance, inductance and electric current respectively, the quantities having the same dimensions of time among the following are
(1)
(2)
(3)
(4)
(1)
(2)
(3)
(4)
Options
- A(1) and (2) only
- B(1) and (3) only
- C(1) and (4) only
- D(1), (2) and (3) only
Correct answer
D. (1), (2) and (3) only
Step-by-step solution
\left[L\right] = \left[ ML^{2}T^{- 2}A^{- 2}\right]and \left[I\right] = \left[M^{0}L^{0}T^{0}A\right]<br /><br />1. \left[ CR\right] = \left[M^{- 1}L^{- 2}T^{4}A^{2}\right]\left[{ML}^{2}T^{- 3}A^{- 2}\right]= \left[M^{0}L^{0}TA^{0}\right]
2. \dfrac{\left[L\right]}{\left[R\right]} = \dfrac{ \left[ML^{2}T^{- 2}A^{- 2}\right]} { \left[ML^{2}T^{- 3}A^{- 2}\right]} = \left[M^{0}L^{0}TA^{0}\right]<br /><br />3. $\left(\sqrt{\text{LC}}\right) = {\left(\left[{ML}^{2} T^{- 2} A^{- 2}\right] × M^{- 1} L^{- 2} A^{2}\right)}$^{1 / 2}
= \left[ M^{0}L^{0}TA^{0}\right]<br /><br />4. \left[ LI^{2}\right] = \left[ML^{2}T^{- 2}A^{- 2}\right]{ \left[ M^{0}L^{0}T^{0}A^{1}\right]}^{2}= \left[ML^{2}T^{- 2}A^{0}\right]