Internal Resistance of a Battery

HOW DOES IT WORK?

Batteries are used in electrical circuits to provide energy per unit charge moving through the circuit. The emf of the battery is measured on a voltmeter connected in parallel with the battery – the battery is not connected to an external circuit. Emf is defined as the maximum amount of work per unit charge that a battery can do.

V_emf =

$\frac{Wmax}{\mathrm{Q}}$

One volt is the potential difference needed when one joule of work is done on one coulomb of charge.

Batteries have internal resistance that depends on the size, chemical properties, age, temperature and the current of the battery. When the battery is connected to components in a circuit, the voltmeter across the terminals of the battery gives a reading smaller than the emf. The reading is known as the terminal or external potential difference.

V_external is smaller than V_emf, because energy per unit charge is needed to allow charged particles to pass through the battery.

V_emf = V_external + V_internal

XPERIMENT 1: DETERMINE THE INTERNAL RESISTANCE OF A BATTERY.           

Time Allocation: 25 Min

The emf of the battery is measured with the voltmeter connected in parallel with the battery. All the switches should be open. The second switch is closed and the readings are taken again. The third switch is now closed and the readings taken again.

The readings are used to draw a graph of potential difference vs current strength.

The equation for a straight line is y = mx + c

From Ohm’s Law: R =

_{$\frac{V}{I}$}

and v = IR

V_emf = V_external + V_internal

V_external = V_emf – V_internal

V_external = V_emf – Ir

V_external = V_emf – rI

The emf of the battery = y – intersect, when the reading on the ammeter = 0 A.

The gradient of the graph is negative, constant and an indication of the internal resistance of the battery.

r = gradient =

_{$\frac{∆y}{∆\chi }$}

EXPERIMENT 2:  COMPARE THE THEORETICAL AND EXPERIMENTAL VALUE OF A NETWORK OF RESISTORS CONNECTED IN SERIES AND PARALLEL.

Time Allocation: 25 Min

Three 1,5 V cells, an ammeter, switch, voltmeter, four resistors with known resistance and a voltmeter are connected as in the diagram.

 

The theoretical resistance is calculated with the following formulae.

_{$\frac{1}{R_p}=\frac{1}{R_2}+\frac{1}{{\displaystyle R_3}}$}

(for parallel combination)

R_t = R_p + R₃ + R₄

The experimental value of the resistance is determined by taking the readings on the ammeter and voltmeter when the switch is closed.

Substitute the readings in the formula R_external =

_{$\frac{V_{Internal }}{I}$}

EXPERIMENT 1: DETERMINE THE INTERNAL RESISTANCE OF A BATTERY.

AIM                                                                                                                         

Time Allocation: 25 Min

To determine the internal resistance of a battery.

MATERIALS:

• Circuit board
• Connecting wires
• Voltmeter
• Ammeter
• Three light bulbs (1.5V)
• Three circuit switches
• Three 1,5 V cells with noticeable internal resistance

 

METHOD:

1. Connect three cells in series.
2. Connect a voltmeter parallel across the terminals of the battery.
3. Connect the bulbs parallel with each other, each with its own switch and in series with the battery and ammeter as per the below drawing.
4. Take the reading on the ammeter and the voltmeter when all the switches are open.
5. Close the switch of one bulb and take the readings on the ammeter and voltmeter.
6. Close the switches of two bulbs and take the readings on the ammeter and voltmeter.
7. Close all switches and take the readings on the ammeter and voltmeter.

CONCLUSION :

Internal resistance was constant and unaffected by the chance in electrical current.

OBSERVATION:

 

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EXPERIMENT 2:  COMPARE THE THEORETICAL AND EXPERIMENTAL VALUE OF A NETWORK OF RESISTORS CONNECTED IN SERIES AND PARALLEL.

AIM                                                                                                                                      

Time Allocation: 25 Min

To compare the theoretical and experimental value of a network of resistors connected in series and parallel.

MATERIALS:

• Circuit board
• Connecting wires
• Voltmeter
• Ammeter
• Three light bulbs
• Switch
• Three 1,5 V cells with noticeable internal resistance

METHOD:

1. First connect three 1, 5 V cells in series.
2. Connect a voltmeter parallel across the terminals of the battery.
3. Connect the ammeter, switch and two resistors in series with two resistors connected in parallel as shown in Figure 1.

1. Take the voltmeter reading when the switch is open.
2. Close the switch. Quickly take the reading on the voltmeter and ammeter again.
3. Open the switch and wait a few minutes for resistors to cool down.
4. Close the switch and take the readings again of R₁, R₂, R₃ and R₄.
5. Obtain four sets of readings according to the diagram.
6. You should therefore connect voltmeter 1 and ammeter 1 for the first reading as shown in Figure 2 and Figure 3 and so on for V2A2, V3A3, V4A4.
7. Determine the average values record the results in the table of question 12 of the Student Practical questioner.
8. Calculate the theoretical resistance is calculated with the following formulae.

_{$\frac{1}{R_p}=\frac{1}{R_1}+\frac{1}{R_2}$}

(for parallel combination)

R_t = R_p + R₃ + R₄

9. Calculate the experimental value of the resistance is determined by taking the readings on the ammeter and voltmeter when the switch is closed.

_{$\frac{1}{R_P}=\frac{1}{R_1}+\frac{1}{R_2}$}

Substitute the readings in the formula R_external =

_{$\frac{V_{\mathit{E}\mathit{x}\mathit{t}\mathit{e}\mathit{r}\mathit{n}\mathit{a}\mathit{l}\mathit{ }}}{I}$}

CONCLUSION:

Theoretical and experimental values of external resistance obtained in the experiment where so close that the deviations where considered negligible and thus both calculated and experimental data can be used.

PRECAUTIONS:

• Do not allow connecting wires to touch as this will cause a surge and this can damage circuit components.
• Do not touch any “live” (connected to the battery) wires directly as this may cause a shock.