MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Ohm's Law in Scalar Form

A resistance ...

Question

A resistance of R $Ω$ draws current from a potentiometer as shown in the figure. The potentiometer has a total resistance $R_{0} Ω$ . A voltage V is supplied to the potentiometer. Derive an expression for the voltage across R when the sliding contact is in the middle of the potentiometer.

Open in App

Solution

As the slide is in middle of the potentiometer only half of its resistance $(R_{0} / 2)$ will be in parallel with the resistance R. Hence, the total resistance $(R_{1})$ will be given by the following expression:

$\frac{1}{R_{1}} = \frac{1}{R} + \frac{1}{(R_{0} / 2)}$

$R_{1} = \frac{R_{0} R}{R_{0} + 2 R}$

The total resistance between $A$ and $C$ is $R_{1} + R_{0} / 2$ .

$∴$ The current flowing through the potentiometer will be

$I = \frac{V}{R_{1} + R_{0} / 2} = \frac{2 V}{2 R_{1} + R_{0}}$

The voltage $V_{1}$ taken from the potentiometer will be the product of current $I$ and resistance $R_{1}$ .

$V_{1} = I R_{1} = (\frac{2 V}{2 R_{1} + R_{0}}) \times R_{1}$

Substituting for $R_{1}$ , we have

$V_{1} = \frac{2 V}{2 (\frac{R_{0} \times R}{R_{0} + 2 R}) + R_{0}} \times \frac{R_{0} R}{(R_{0} + 2 R)}$

$V_{1} = \frac{2 V R}{2 R + R_{0} + 2 R}$

$V_{1} = \frac{2 V R}{R_{0} + 4 R}$

Suggest Corrections

thumbs-up

21

Similar questions

Q. A resistance of

R

draws the current form of the potentiometer. The potentiometer wire,

A B

, has a total resistance of

R_{0}

V

is supplied to the perpendicular. Derive an expression for the voltage across

R

when the sliding contact is in the middle of potentiometer wire.

Q. A resistance of

R

drawn current from a potentiometer . The potentiometer wire,

A B

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.

Q. Answer the following :
(a) Why are the connections between the resistors in a meter bridge made of thick copper strips?
(b) Why is it generally preferred to obtain the balance point in the middle of the meter bridge wire?
(c) Which material is used for the meter bridge wire and why?
OR
A resistance of R

Ω

draws current from a potentiometer as shown in the figure. The potentiometer has a total resistance

R_{0} Ω

. A voltage V is supplied to the potentiometer. Derive an expression for the voltage across R when the sliding contact is in the middle of the potentiometer.

Q. A battery of

V

voltage is connected across the potentiometer wire

A C

of total resistance

R_{0}

as shown. Calculate the potential across the resistance

R

if the sliding contact point

B

is exactly at the middle of the potentiometer wire.

V_{0}

is applied to a potentiometer whose sliding contact is exactly in the middle. A voltmeter

V

is connected between the sliding contact and one fixed end of the potentiometer. It is assumed that the resistance of the voltmeter is not very high in comparison to the resistance of the potentiometer wire. What voltage will the voltmeter show : higher than, less than, or equal to

V_{0} / 2

?

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Ohm's Law in Scalar Form

PHYSICS

Watch in App

explore_more_icon

Explore more

Ohm's Law in Scalar Form

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon