## To calibrate an ammeter using D.C. slide wire potentiometer.

**OBJECT:** To calibrate an ammeter using D.C. slide wire potentiometer.

**APPARATUS REQUIRED: **Potentiometer

**THEORY:**

The electromotive force (emf) of a cell is its terminal voltage when no current is flowing through it. The terminal voltage of a cell is the potential difference between its electrodes. A voltmeter cannot be used to measure the emf of a cell because a voltmeter draws some current from the cell. To measure a cell's emf a potentiometer is used since in a potentiometer measurement no current is flowing. It employs a null method of measuring potential difference, so that when a balance is reached and the reading is taken, no current is drawn from the source to be measured this is the basic circuit diagram for a potentiometer. Point C is the sliding contact which can be adjusted for zero current deflection through the galvanometer. In this method a uniform, bare slide wire AB is connected across the power supply. If you were to connect a voltmeter between the + power supply terminal and point A you would measure essentially zero volts. If you were to now connect the voltmeter between the + power supply and point B you would measure a voltage equal to the terminal voltage of the power supply which is approximately 2.5volts. The potential relative to point A then varies from zero at A to approximately 2.5 volts at B. The cell whose emf is to be determined is then connected so that its emf opposes the potential along the wire. At some point C the potential difference between A and C is exactly equal to the emf of the cell so that if the other terminal of the cell is connected to the point C, no current will flow. The calibration procedure is to locate this point C using a standard cell whose emf is accurately known (emf = 1.0186 volts). You then know that at this point C the potential difference relative to point A is exactly 1.0186 volts. Since the wire is uniform, the length of wire spanned is proportional to the potential drop and the wire can now be calibrated in volts per cm. The emf of an unknown cell is then found by finding a new point C whose potential is exactly equal to the emf of the unknown cell and multiplying this new distance AC times the calibration factor determined using the standard cell. It is crucial in this experiment that the current flowing through wire AB remains constant throughout the experiment. If the current varies then the potential at all points along the wire will vary and you cannot trust your calibration. An ammeter is included in series with wire AB so that you can monitor this current. The circuits used in this experiment are shown below

Since the electromotive force of the standard cell is equal to the potential drop in the length of wire spanned (measured from A) for a condition of balance and the same is true for the unknown cell, the emf of each cell is proportional to the lengths of wire spanned. Thus

And the unknown emf is given by

where _{x} is the unknown emf and, is the emf of the standard cell, *L*_{x} is the length of wire (AC) used for balancing the unknown cell, and *L*_{s} is the length of wire used for balancing with the standard cell. If we have a test cell of emf, and internal resistance *r* supplying current to a variable load resistor *R* then we will measure a terminal voltage *V* which is a function of the load resistance *R*.

**CIRCUIT DIAGRAM:**

Fig. 4.1 Potentiometer

**PROCEDURE**

- Calibration

Use the experimental arrangement shown in Figure 2 for the calibration of the potentiometer wire, using the standard cell. Start with your sliding contact C near the center of the bridge. Press the contact C. The galvanometer will probably deflect. Find a point C where there is no deflection. Now close switch K1 and again adjust C for no deflection. Pushbutton switch K1 (Figure 2) shorts out the protective resistance R1 and gives the galvanometer maximum sensitivity. Record the final setting of the contact point C and known value of the emf of the standard cell. Compute the calibration factor f in volts/cm.

- Electromotive force (emf) of a test cell

Connect the test cell into the circuit as shown in Figure 3. Determine the emf of this cell by again locating a point C where no galvanometer deflection occurs when contact C is pressed. Remember to close switch K1 for a finer adjustment of C. When no galvanometer deflection occurs with the switch K1 closed the potential drop along the wire from A to C exactly equals the emf of the test cell. Record the final balance position of the contact C and the emf of the test cell.

- Terminal Voltage of the test cell in use

Now adjust the load resistor *R* to 150 ohms. You must hold switch K2 down in order for the circuit connecting *R* across the test cell to be complete. While holding K2 down again balance the bridge as described above. When balanced, again record the distance AC and compute the terminal voltage of the test cell. Repeat this procedure for *R* = 100, 60, 30, 15, 10, 8, 6, and 4 ohms. Using your measured value for the terminal voltage *V* and the resistance *R*, compute the current *I* being supplied by the test cell for each value of *R* used.

Plot a graph with terminal voltage *V* on the vertical axis and current on the horizontal axis. Draw the best straight line through your data points. Determine the value of the internal resistance of the test cell from this graph.

**RESULTS: **

*R*= ____________ AC = ____________*V*= ____________*I*= ____________*R*= ____________ AC = ____________*V*= ____________*I*= ____________

**Internal resistance of test cell from graph: r = ____________**

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