Question:
If \(Q\), \(L\) and \(T\) represent the electric charge, inductance and time respectively, then the physical quantity having the dimensions of \( \dfrac{QL}{T^2} \) is:
If \(Q\), \(L\) and \(T\) represent the electric charge, inductance and time respectively, then the physical quantity having the dimensions of \( \dfrac{QL}{T^2} \) is:
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Remember:
\[
Q = IT
\]
and
\[
V = \frac{W}{Q}
\]
These relations are extremely useful in dimensional analysis problems involving electrical quantities.
Updated On: Jun 17, 2026
- Magnetic energy
- Impedance
- Electric potential
- Electric field
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The Correct Option is C
Solution and Explanation
Concept:
Dimensional analysis is a very powerful mathematical tool in physics which helps in identifying the nature of physical quantities from their dimensional formulae.
The dimensional formula of inductance is:
\[
[L] = \frac{ML^2T^{-2}}{A^2}
\]
Also, electric charge is related to current by:
\[
Q = IT
\]
Hence,
\[
[Q] = [AT]
\]
We are required to determine the dimensions of:
\[
\frac{QL}{T^2}
\]
Step 1: Substitute the dimensions of charge and inductance. \[ \left[\frac{QL}{T^2}\right] = \frac{(AT)\left(\dfrac{ML^2T^{-2}}{A^2}\right)}{T^2} \] \[ = \frac{ML^2T^{-1}}{AT^2} \] \[ = ML^2T^{-3}A^{-1} \]
Step 2: Compare this dimensional formula with known physical quantities. The dimensional formula of electric potential is: \[ [V] = \frac{\text{Work}}{\text{Charge}} \] \[ = \frac{ML^2T^{-2}}{AT} = ML^2T^{-3}A^{-1} \] This exactly matches the obtained dimensions. Therefore, the required quantity is: \[ \boxed{\text{Electric potential}} \]
Step 1: Substitute the dimensions of charge and inductance. \[ \left[\frac{QL}{T^2}\right] = \frac{(AT)\left(\dfrac{ML^2T^{-2}}{A^2}\right)}{T^2} \] \[ = \frac{ML^2T^{-1}}{AT^2} \] \[ = ML^2T^{-3}A^{-1} \]
Step 2: Compare this dimensional formula with known physical quantities. The dimensional formula of electric potential is: \[ [V] = \frac{\text{Work}}{\text{Charge}} \] \[ = \frac{ML^2T^{-2}}{AT} = ML^2T^{-3}A^{-1} \] This exactly matches the obtained dimensions. Therefore, the required quantity is: \[ \boxed{\text{Electric potential}} \]
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