9.1 Die emk en interne weerstand van 'n sekere battery is eksperimenteel bepaal - NSC Physical Sciences - Question 9 - 2017 - Paper 1

To determine the best fit line through the given points on the graph, plot the data points corresponding to the measured current (I) and potential difference (V). The line should be drawn in such a way that it is as close as possible to most of the points while intercepting both axes. Ensure that the line has a consistent slope, maintaining a linear relationship.

From the graph, identify the y-intercept of the best fit line. This y-intercept represents the electromotive force (ε) of the battery. If the line intercepts the y-axis at approximately 5.5 V, then:

$ε = 5.5 ext{ V}$

Using the slope of the best fit line from the graph, which can be calculated as: ext{slope} = rac{ΔV}{ΔI} where ΔV is the change in potential difference and ΔI is the change in current. Based on this slope, the internal resistance (r) can be found using the formula: R_{int} = rac{ε - V_{ext}}{I_{ext}} where V_{ext} is the external voltage and I_{ext} is the external current.

To find the current flowing through the 8 Ω resistor, use the formula: I = rac{V}{R} where V is the voltage reading from the voltmeter (21.84 V) across the 8 Ω resistor. Thus: I = rac{21.84 ext{ V}}{8 ext{ Ω}} = 2.73 ext{ A}

The equivalent resistance (R_eq) of resistors in parallel is calculated using: rac{1}{R_{eq}} = rac{1}{R_1} + rac{1}{R_2} For this case, substituting R1 = 30 Ω and R2 = 20 Ω: rac{1}{R_{eq}} = rac{1}{30} + rac{1}{20} Solving, we find: $R_{eq} = 12 ext{ Ω}$

To find the internal resistance r of the battery, use: r = rac{ε - V_{ext}}{I_{ext}} Substituting ε = 60 V, V_{ext} = V_{total} - V_{internal} = 54.6 V, and I_{ext} = 2.73 A, we derive:

The heat (Q) generated in the circuit can be calculated using: $Q = I^2 imes R imes t$ where t is the time in seconds (0.2 s). Inserting values: $Q = (2.73 ext{ A})^2 imes 8 Ω imes 0.2 ext{ s}$ This yields: $Q ext{ is approximately } 29.81 ext{ J}$