Potentiometers are used to measure the emf provided by a source without affectin

Question

Potentiometers are used to measure the emf provided by a source without affecting the emf by drawing current from the source as a non-ideal voltmeter would. The potentiometer circuit shown below demonstrates how it works. The resistor R is a wire of known length & constant cross section connected to source of known emf. Contact c can be slid along legnth of the wire and conected to unknown source of emf, x. Bottom loop also contains ammeter. Contact c is then moved until ammeter measure 0 current.

a. If curent Ix = 0, what is current through top loop in terms of R and ?

b. Find relationship between x & I.

c. Source of known emf 2 replaces x and slider is moved until current through bottom branch disappears so I2 = 0. What is now the current through top loop?

d. Find a relation between 2 and R2 , the new resistance between point a & c.

e. Using information worked out in part a, b, c show that x = ( Rx / R2 ) 2 .

f. If length ac = 33.6 cm , length ac = 45.8 cm, total length of resistor R = 100 cm, 2 = 1.0182 V, calculate unknown emf.

Explanation / Answer

a.) If curent Ix = 0, what is current through top loop in terms of R and ?

since the current Ix = 0, the current through top loop would be I.

Now, I = applying Kirchoff's Voltage Law (KVL) in the top loop we get:

- IR = 0

or I = /R which is current through top loop in terms of R and .

b.) Find relationship between x & I.

Contact c moves along the legnth of the wire until ammeter measure 0 current. At this moment aplying KVL in the lower loop gives

IRx - x = 0 (as Ix = 0)

or x = IRx where Rx is the resistance in the length of the wire where the Contact c shows Ix = 0

(c.)

We apply KVL in the top loop and get:-

   = IR

Now, applying KVL in the bottom loop gives

2 = IR2

So I = 2/R2 is the current through top loop

(d.)

From (c) we got

= IR and

2 = IR2

solving these two equations we get

/2 = R/R2

or 2 = (R2)/R ..

feel free to ask if anything is left out by me.......

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