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

Aspect 2 & 3

Data Collection and Processing

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...