# Internal Resistance and EMF of a Battery Cell

**Topics:**Accuracy and precision, Analytic geometry, Battery

**Pages:**8 (840 words)

**Published:**November 29, 2014

DCP

ASPECT 1

SYMBOLS:

Internal resistance of the battery: r

External variable resistor: R

Voltage: V

EMF of the battery: E

Current: I

FORMULA

V= IR

E = I (R+r)

E = IR +I ⋅ r

E = V + I ⋅ r

V = E - I ⋅ r

V = -r ⋅ I +E

_Graph of V against I will be plotted in order to_ _determine the internal resistance and EMF of the battery. The slope will be -r and the intercept vertical axis will be the EMF (E)._

REFERENCE VALUE

EMF of the battery

1. 490 ± 0.001V

ASPECT 2 & 3

DATA COLLECTION AND PROCESSING

Obs. No.

Voltage

Current

± 0.01V

± 0.1A

1

0.42

1.7

2

0.54

1.5

3

0.62

1.3

4

0.66

1.2

5

0.80

0.9

6

0.90

0.7

7

0.94

0.6

8

1.10

0.4

9

1.20

0.3

Figure 1 Voltage against Current

CEV

CALCULATION

_THE INTERNAL RESISTANCE OF THE BATTERY_

Uncertainty for Slope

From the graph above (Voltage against Current)

Slope of the best-fit line= - 0.5223 Ω (from the graph)

S1 = maximum slope = - 0.4714 Ω (from the graph)

S2 = minimum slope = - 0.6429 Ω (from the graph)

ΔS = |S1 - S2| / 2

= | (-0.4714 - (-0.6429)) | / 2

= 0.08580 Ω (cor. to 4 sig. fig)

_THE INTERNAL RESISTANCE OF THE BATTERY ± Δ INTERNAL RESISTANCE OF THE BATTERY = 0.5223 Ω ± 0.08580 Ω_ (COR. TO 4 SIG. FIG)

Percentage precision

= (1.000 - 0.08580 /0.5223) x 100% = 83.57% (cor. to 4 sig. fig)

_THE EMF OF THE BATTERY_

Uncertainty for intercept vertical axis

From the graph above (Voltage against Current)

Intercept vertical axis of the best-fit line = 1.2969 V (from the graph)

y1 = Intercept vertical axis of the maximum slope = 1.2414 V (from the graph)

y2 = Intercept vertical axis of the minimum slope = 1.4929 V (from the graph)

Δy = |y1 - y2| / 2

= | (1.2414V - 1.4929V) | / 2

= 0.25150 V (cor. to 5 sig. fig)

_THE EMF OF THE BATTERY ± Δ EMF OF THE BATTERY = 1.2969 V ± 0.25150V_ (COR. TO 5 SIG. FIG)

Percentage precision

= (1.0000 - _0.25150_/_1.2969_) x 100% = 80.61% (cor. to 4 sig. fig)

Percentage accuracy

= (1.0000 - (1. 4900 - _1.2969_ /1. 4900)) x 100% = 87.05% (cor. to 4 sig. fig)

CONCLUSION AND EVALUATION

_ASPECT 1_

CONCLUSION

The Internal resistance of the battery

_0.5223 Ω ± 0.08580 Ω (cor. to 4 sig. fig)_

Percentage precision

83.57% _(cor. to 4 sig. fig)_

The EMF of the battery

_1.2969V ± 0.25150V (cor. to 5 sig. fig)_

Percentage precision

_80.61% (cor. to 4 sig. fig)_

Percentage accuracy

_87.05% (cor. to 4 sig. fig)_

The percentage precision of measuring the internal resistance of the battery is 83.57%, with the internal resistance 0.5223-Ω ± 0.08580 Ω. On the other side, the percentage precision of measuring the EMF of the battery is 80.61% with the EMF 1.2969V ± 0.25150V. The percentage accuracy is 87.05%, with the reference value of 1.490. The results are satisfactory since in the experiment, precise tools are used. . The values found in the experiments are precise and they are as expected.

COMMENT ON THE GRAPH

In the Voltage against Current graph, the best-fit line cannot perfectly pass through all the points. The maximum slope and the minimum slope is not stick to the slope of the best-fit line. The uncertainties of the y-axis in the graph are too small that cannot be seen. However, the uncertainties of the x-axis can be seen obviously in the graph.

The intercept vertical axis will show the EMF of the battery. The y-intercept of the best-fit line is 1.2969. The y-intercept of the maximum slope is 1.2414. The y-intercept of the minimum slope is 1.4929.

_ASPECT 2 & 3_

THE CONTRIBUTION TO THE PRECISION AND ACCURACY OF EACH MEASURED VARIABLE

Voltage (V)

± 0.01V

Current (I)

± 0.1A

The y-intercept of the graph, which shows the EMF of the battery, is expected to be the reference...

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