Question

The unit and dimensions of impedance in terms of charge Q are

A. Mho, \[[M{L^2}{T^{ - 2}}{Q^{ - 2}}]\]
B. Ohm, \[[M{L^2}{T^{ - 1}}{Q^{ - 2}}]\]
C. Ohm, \[[M{L^2}{T^{ - 2}}{Q^{ - 1}}]\]
D. Ohm, \[[ML{T^{ - 1}}{Q^{ - 1}}]\]

Answer 1

Hint:
- Convert the impedance equation in terms of charge, Q.
- You should know the definition of voltage.
- You should know the definition of impedance.

Complete step by step solution:
Impedance: Impedance is a kind of resistance or opposition to the flow of AC current because of any three components that are resistive, inductive or capacitive. It is a combination of both resistance and reactance in a circuit. Resistance is simply defined as the opposition to the flow of electric current in the circuit.Resistance can be seen in both AC and DC circuits.Impedance can be seen only in AC circuits.Resistance is caused due to the electrons in a conductor colliding with the ionic lattice of the conductor which results in the conversion of electrical energy in heat. It could be said that electrical resistance is the opposition to steady electric current. An ideal resistance does change with frequency when connected with DC.Impedance is the measure of the nature of opposition of the AC electricity which is created due to inductance and capacitance. This opposition varies with the frequency. Very often, reactance and impedance are thought to be the same and are interchangeably used. It is important to understand that reactance is the resistance offered to the AC current by inductors and capacitors only while impedance is the sum of the resistance and reactance.

Dimension:It is an expression that relates derived quantity to fundamental quantities.The fundamental dimensions used in mechanics are time, mass, and length. Symbolically, these are written as t, m, and l, respectively. The study of electromagnetism adds an additional fundamental dimension, electric charge, or q. Other quantities have dimensions compounded of these.
- Unit of impedance is ohm and
- Dimension of Impedance\[ = \dfrac{V}{I}\]
               \[ = \dfrac{W}{{QI}}\]
\[ = \dfrac{{\left[ {M{L^2}{T^{ - 2}}} \right]}}{{\left[ {QQ{T^{ - 1}}} \right]}}\] Where dimension of W \[ = \left[ {M{L^2}{T^{ - 2}}} \right]\] and \[I = \left[ {Q{T^{ - 1}}} \right]\]
\[ = [M{L^2}{T^{ - 1}}{Q^{ - 2}}]\]



Note:
- Try to make the equation in terms of Q before going for dimension.
- Take care of signs while going to the numerator.
- Try to memorize basic dimensions.