CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

A resistance of $$R$$ drawn current from a potentiometer . The potentiometer wire, $$AB$$ has a total resistance of $$R_0$$ A voltage V is supplied to the potentiometer . Derive an expansion for the voltage across $$R$$ when the sliding contact is in the middle of potentiometer wire.
1050453_034046c247574bcca3a2d065cd0c1e0b.png


Solution

Given, $$Resistance =R,Potentiometer =AB,Voltage=V$$

When the slides are in the middle of the potentiometer only half of its total resistance i;e $$\dfrac{R_0}{2}$$ will between A and B,

So, $$\dfrac{1}{R}=\dfrac{1}{R}+\dfrac{1}{\dfrac{R_0}{2}}\Rightarrow R_1=\dfrac{R_0R}{R_0+2R}$$

The total resistance between the A and B is  will be the sum of the resistance between A and C or C and B,

$$R_1+\dfrac{R_)}{2}$$

The current is following through the potentiometer will be:

$$I=\dfrac{V}{R_1+\dfrac{R_0}{2}}=\dfrac{2V}{2R_1+R_0}$$

The voltage $$V_1$$taken from the potentiometer will be product of the current $$I$$ and the resistance $$R_1$$,

$$V_1=IR_1=\dfrac{2V}{2(\dfrac{R_0R}{R_0+2R})+R_0}\times(\dfrac{R_0R}{R_02R})$$

$$V_1=\dfrac{2VR}{2R+R_0+2R}=\dfrac{2VR}{R_0+4R}$$

987934_1050453_ans_585ec94308f84866b6fa16aafef7d597.png

Physics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image