Question:
Which of the following units denotes the dimensions $[ML^2/Q^2],$ where $Q$ denotes the electric charge ?
Which of the following units denotes the dimensions $[ML^2/Q^2],$ where $Q$ denotes the electric charge ?
Updated On: Jul 5, 2022
- $Wb/m^2$
- henry (H)
- $H/m^2$
- weber (Wb)
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The Correct Option is B
Solution and Explanation
Magnetic energy $=\frac{1}{2}Li^{2}=\frac{LQ^{2}}{2t^{2}}$
[$L \rightarrow$ inductance, $i \rightarrow$ current]
Energy has the dimensions $[ML^2T^{-2}].$
Equate the dimensions, we have
$\left[ML^{3}T^{-2}\right]=\left(henry\right)\times \frac{\left[Q^{2}\right]}{\left[T^{2}\right]}$
$\Rightarrow \left[henry\right]=\frac{\left[ML^{2}\right]}{\left[Q^{2}\right]}$
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Concepts Used:
Inductance
Inductance is a key parameter in electrical and electronic circuit designs. Like resistance and capacitance, it is a basic electrical measurement that affects all circuits to some degree.
Inductance is used in many areas of electrical and electronic systems and circuits. The electronic components can be in a variety of forms and may be called by a variety of names: coils, inductors, chokes, transformers, . . . Each of these may also have a variety of different variants: with and without cores and the core materials may be of different types.
There are two ways in which inductance is used:
- Self-inductance: Self-inductance is the property of a circuit, often a coil, whereby a change in current causes a change in voltage in that circuit due to the magnetic effect of caused by the current flow. It can be seen that self-inductance applies to a single circuit - in other words it is an inductance, typically within a single coil. This effect is used in single coils or chokes.
- Mutual-inductance: Mutual inductance is an inductive effect where a change in current in one circuit causes a change in voltage across a second circuit as a result of a magnetic field that links both circuits. This effect is used in transformers.