Physics for the Life Sciences
Experiment 49
The Slide-wire Potentiometer
Purpose

To study the operation of a potentiometer circuit and to use it to determine the emf and internal resistance of a dry cell.

Apparatus

Slide wire potentiometer     Galvanometer     Resistance box (0 - 100 W)

Power supply (6 to 12 V DC)     Ammeter(1 A DC)     Standard cell

Single pole, double throw switch     1½ V dry cell (D or C size)

Variable resistor (100 W)     Connecting wires

Theory

Whenever a voltmeter is used to measure the potential difference across part of an electrical circuit, the effective resistance of that part of the circuit is altered and the current in it changes since some of the current is needed to actuate the meter. These changes in the circuit can be minimized by using a very high resistance voltmeter. There are some instances, however, when we need to measure a potential difference without drawing any current from the circuit at all. One of these is the measurement of the electromotive force of a cell. This is the potential difference across the terminals of the cell when no current is taken from it; that is an open circuit. A potentiometer is a device which allows measurements of potential difference without drawing any current from the circuit. It is a null method. The circuit of a potentiometer is shown below.

A simple potentiometer circuit consists of a uniform slide wire, AB, usually 1 m long through which a constant current is maintained by a power supply. The cell or battery whose emf is to be measured, E_x is connected through a galvanometer, G, to the slider, C. A balance condition exists when the potential difference across AC is just equal to the emf of the cell, E_x in which case there will be no deflection on the galvanometer. This procedure is then repeated with a standard cell of known emf, C, so that the wire may be calibrated.

Suppose L_s is the length AC when the standard cell of emf E_s is used, and L_x is the length for the unknown cell of emf, E_x, then E_x/E_s =L_x/ L_s, or

E_x = E_s(L_x/L_s)............................................................................................... (1)
The value of an unknown emf may then be determined from the measurements of L_x and L_s, if the standard emf, E_s is known.

It is often convenient to adjust the current through the wire AB so that the potential difference across it is a certain value such as exactly 1 V. In this case, each cm along the wire represents 0.01 V or 10 mV and each mm represents 1 mV. Commercial potentiometers are designed this way so that the potential difference to be determined may be measured directly on a dial calibrated in volts or millivolts.

When current is drawn from a cell or battery, the potential difference across its terminals decreases as the current from it increases. This is due to the internal resistance within the battery. The difference between the emf of the cell on open circuit and the potential difference across its terminals when delivering a current I, is then equal to the potential difference across its internal resistance, Ir. Thus E- V = Ir, or r = (E - V)/I. The value of the internal resistance of a cell may then be determined by measuring its emf, E, and its terminal potential difference, V, while a current I is being drawn from it. The current drawn from a cell of emf E when an external resistance R is connected across it is given by Ohm's law; I = E/(R + r) where r is the internal resistance of the cell.
Hence r = (E - V)/I = (E - V)(R + r)/E, or, solving for R,

R = (R/V)E - r ........................................................................ (2)

This is a linear equation of R with R/V. A graph of R (on the y-axis) versus R/V (on the x-axis) should then be linear with a slope equal to the emf, E. The negative intercept on the R axis is equal to the internal resistance, r.



Procedure

1. Connect up the circuit as shown with the key K open and the power supply switched off. Have your instructor check your circuit.
2. Switch on the power supply with the standard cell, E_s, connected to the circuit. Adjust the slider, C, to the 50 cm mark and adjust the current through the potentiometer wire until there is a null reading on the galvanometer when the key is depressed. Record the reading of the ammeter current. This reading should be checked periodically throughout the experiment and the variable resistor adjusted as needed to keep this value constant. Record the emf of the standard cell in the table.
3. Close the switch K so as to connect the dry cell as the unknown, E_x, in the circuit instead of the standard cell. Readjust the position of the slider until a null reading on the galvanometer is found. Record this position of the slider in the table.
4. Leave the dry cell in the circuit as you have it now and connect the resistance box in parallel with it. Adjust the value on the box to 20W and determine the slider position for a null reading on the galvanometer. Record the length AC.
5. Decrease the value on the resistance box to 18W then in steps of 2W down to 10W, and in steps of lW down to 3W . In each case, measure the slider position for a null reading on the galvanometer and enter the data in the table.
6. Disconnect the resistance box and remeasure E_x for the dry cell.

Calculations

1. Determine the potential difference per cm along the potentiometer wire and enter the result in the table.
2. Calculate the emf of the dry cell from the value of L_x obtained in procedure (3).
3. Calculate the terminal voltage of the dry cell for each value of R in procedure (5) and the corresponding values of R/V.
4. Plot a graph of R versus R/V. Determine the emf of the dry cell from the slope of the graph and the value of the internal resistance from the negative intercept.

Data

Resistance R (W)	Length Lx (cm)	Terminal Voltage V	R/V (A-1)
20
18
16
14
12
10
9
8
7
6
5
4
3
infinite

Current through galvanometer wire................................................................ ______ A

Emf of standard cell......................................................................................... ______ V

Balance length for dry cell (L_x)....................................................................... ______ cm

Emf of dry cell.................................................................................................. ______ V

Potential difference per cm along potentiometer........................................... ______ mV/cm

Emf of dry cell determined from slope of graph............................................. ______ V

Internal resistance of dry cell determined from graph.................................. ______ W

Emf of dry cell at end of experiment.............................................................. ______ V



Questions

1. Compare the measured values of the emf of the dry cell obtained procedure (3) with that determined from the slope of the graph. Explain any differences in the values. How does the value of the emf as measured in procedure (6) compare with these? Why is this?
   
   
   
   
   
   
   
   
2. What is the distinct advantage of using a potentiometer to measure the value of an emf of a source over other methods?
   
   
   
   
3. A Potentiometer was used to measure the emf E and internal resistance r of an unknown battery. With a standard cell of emf 1.0195 V, the balance Position was at 22.1 cm. With the unknown battery, the balance position was at 65.0 cm. When a 10 W resistor was connected directly across the battery, the balance position dropped to 54.2 cm. What were the values of E and r for the battery?
   
   
   
   
   
   
   
   
   
   
   
   

© Dr. John Askill, 1999.             webmaster