Answer
405k+ views
Hint:A potentiometer is an instrument used for measuring an electromotive force by balancing it against the potential difference produced by passing a known current through a known variable resistance. Find the current using ohm’s law. Potential gradient is the ratio of potential across potentiometer to the length of the potentiometer.
Complete step-by-step solution:
Potentiometer wire length, $l = 4\,m$
Resistance of the potentiometer, $R = 10\Omega $
Emf of the cell, $E = 3\,V$
We know that the potential gradient is the ratio of the potential difference across the potentiometer to the length of the potentiometer. The potential difference across the circuit is the same as the emf of the cell.
The potential gradient $k$ will be given as:
$k = \dfrac{V}{L}$
Here, $V$ is the potential difference which is the same as the emf of the cell. Substituting the values, we get
$k = \dfrac{{3V}}{{4m}}$
$ \Rightarrow k = 0.75\,V{m^{ - 1}}$
Therefore, the potential gradient of wire is $0.75\,V{m^{ - 1}}$ .
Thus, option A is the correct option.
Additional details: A potentiometer is a three-terminal resistor which has a sliding or rotating contact that forms an adjustable voltage divider. When only two terminals are used, one end and the wiper, it acts as a variable resistor or rheostat. A potentiometer is a measuring instrument which is essentially a voltage divider used for measuring electric potential (voltage); the component is an implementation of the same principle, hence its name. It is commonly used to control electrical devices such as volume controls for audio equipment.
Note:There is no use of the resistance given in the problem to find the value. Though without the resistance the circuit will not act as a potentiometer. The unit of potential gradient is $V{m^{ - 1}}$ . Potentiometer can also be considered as an absolute position sensing device.
Complete step-by-step solution:
Potentiometer wire length, $l = 4\,m$
Resistance of the potentiometer, $R = 10\Omega $
Emf of the cell, $E = 3\,V$
We know that the potential gradient is the ratio of the potential difference across the potentiometer to the length of the potentiometer. The potential difference across the circuit is the same as the emf of the cell.
The potential gradient $k$ will be given as:
$k = \dfrac{V}{L}$
Here, $V$ is the potential difference which is the same as the emf of the cell. Substituting the values, we get
$k = \dfrac{{3V}}{{4m}}$
$ \Rightarrow k = 0.75\,V{m^{ - 1}}$
Therefore, the potential gradient of wire is $0.75\,V{m^{ - 1}}$ .
Thus, option A is the correct option.
Additional details: A potentiometer is a three-terminal resistor which has a sliding or rotating contact that forms an adjustable voltage divider. When only two terminals are used, one end and the wiper, it acts as a variable resistor or rheostat. A potentiometer is a measuring instrument which is essentially a voltage divider used for measuring electric potential (voltage); the component is an implementation of the same principle, hence its name. It is commonly used to control electrical devices such as volume controls for audio equipment.
Note:There is no use of the resistance given in the problem to find the value. Though without the resistance the circuit will not act as a potentiometer. The unit of potential gradient is $V{m^{ - 1}}$ . Potentiometer can also be considered as an absolute position sensing device.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)