Question

SI unit of potential gradient is ________
(A). $Vcm$
(B). $\dfrac{V}{{c{m^2}}}$
(C). \[Vm\]
(D). \[\dfrac{V}{m}\]

Answer 1

- Hint: In order to know the unit of potential gradient first we may need to know what is potential gradient and its definition. After that we will calculate its unit and see what its SI unit is?

Complete step-by-step solution -
As we know the term potential gradient may be defined as the rate of change of potential with respect to the displacement or gradient.
Mathematically given by :
$E = - \dfrac{{dv}}{{dx}}$
 Where,
E = potential gradient
dv - change in potential (in volts)
dx- change is distance (in meters)
Now, to calculate the unit of potential gradient, we will replace the unit of above terms in given formula
As mentioned above the unit of voltage is volt and the unit of distance is meter.
Substituting these values in the above equation we will get
$E = \dfrac{{volt}}{{meter}}$
As seen above, there is no term to cancel each other and hence the unit of potential gradient will be volt per meter.
Hence the correct answer is ”D”.

Additional Information-
In order to increase the sensitivity of potentiometer i.e. to get the null point easily we should have a smaller potential gradient. Potentiometer-This terminology (potential gradient) is mainly used in potentiometers which is a device that gives the true reading of voltage across any element. Also, a potentiometer is more sensitive when the null point is near the midpoint of the potentiometer. The term potential gradient is related to flux.

Note- As we calculated the unit of potential gradient in the same manner we can calculate the unit of other terms like force, momentum etc. that is we can derive the unit of the quantities from the formula. And we know that there are 9 fundamental quantities while the other are derived quantities.