Activity: Internal resistance of battery [Printable view]

Key Learning Points:
1.   Internal resistance of battery
2.   Voltage, current and resistance in simple circuit
3.   Ohm's law and voltage drop across resistor
4.   Resistors in series and in parallel

Introduction:

 A way to represent the internal resistance of a battery in a circuit.

If you use a voltmeter to measure the open circuit emf of an AA size carbon zinc battery, you will find that the emf is about 1.5 V. But if you are using a circuit to draw a large current from the battery, you will find that the voltage across the battery is less than 1.5 V. This is because the battery itself has an intrinsic resistance called internal resistance. One way to think of internal resistance is to imagine a real battery as being made up of an ideal battery of emf V0, connecting in series with a resistor r which represents the internal resistance (see the figure). When no current is drawn from the battery, the voltage drop across the battery is of course V0. But when a current I is drawn from the battery, there is a voltage drop I r across the resistor, so the voltage drop V across the battery is decreased to

 V = V0 - I r (1)

Hence the larger the current drawn, the smaller the emf of the battery. The internal resistance of a battery is usually quite small. For example, the internal resistance of a typical carbon zinc AA battery is approximately 0.5 W at 21 oC [1].

Battery manufacturers need a quick and well-designed method to test a large number of batteries. In this activity, we are going to measure the internal resistance of an AA size carbon zinc battery using a method similar to that used by battery manufacturers.

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Background information

The method used is called the voltage drop method [2]. Consider the circuit as shown in the figure. When the switch is open, a current I1 is drawn from the battery. From equation (1), the voltage drop V1 across the battery is given by

 V1 = V0 - I1 r (2)

When the switch is closed, the resistance of the external circuit decreases, because there are now two resistors connected in parallel. A different set of voltage drop and current,V2 and I2, will be obtained with the relationship

 V2 = V0 - I2 r (3)

Subtracting equation (3) from equation (2), we have

V1 - V2 = (I2 - I1) r
or
 r = V1 - V2 I2 - I1
(4)

The internal resistance of the battery can be calculated from equation (4).

In the experiment you are about to do, the resistance values of the load resistors used and the procedure of the measurement are modelled after a standardised test used by battery manufacturers [1].

 Video of the experiment
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Apparatus:

AA size carbon zinc battery, battery holder, resistor with high resistance (about 750 W), resistor with low resistance (about 4 W), voltmeter, milliammeter, ammeter, (one can use digital multimeters instead), switch, and connecting wires

 Experimental setup Circuit diagram

Procedures:

1. Set up the circuit as shown in the above figure. Do not place the battery into the battery holder at this moment. Keep the switch open.
2. Place the carbon zinc battery in the battery holder. A current will flow through the 750 W resistor. Record the readings of the voltmeter and the milliammeter (V1 and I1) when the readings become stable.
3. Change the milliammeter to an ammeter which is able to measure current of about 0.5 A. Make sure the ammeter you use is of suitable scale or you may damage the ammeter.
4. Close the switch so that currents flow through both the 4 W resistor and 750 W resistor. Record the readings of the voltmeter and the ammeter (V2 and I2) about one second after the switch is closed.
5. Open the switch and remove the battery from the battery holder after the required measurements are completed.
6. Calculate the internal resistance of the carbon zinc battery using equation (4).

Discussion:

1. What was the emf rating of the battery you used? What was the voltage measured when a small current was being drawn? What was the voltage measured when a large current was being drawn (when the switch was closed)?
2. How did the internal resistance you obtained in this experiment compare with the typical value of 0.5 W for an AA size carbon zinc battery?
3. Do the two load resistors need to be 4 W and 750 W in order for the internal resistance measurement to be accurate? If, say, a 5 W resistor and a 1000 W resistor are used instead, will the measured internal resistance become inaccurate?
4. What are the main sources of experimental error for this experiment?

 [1] Energizer Engineering Datasheethttp://data.energizer.com/PDFs/1215.pdf [2] Energizer Battery Application Manual, Internal Resistance sectionhttp://data.energizer.com/PDFs/carbonzinc_appman.pdf