Internal Resistance and EMF of a Battery Cell

EM6 INTERNAL RESISTANCE AND EMF OF A BATTERY CELL

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