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
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