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This problem involves a meter bridge circuit. The total length of the meter bridge wire is l = 1000 mm. The known resistor is R = 680 . The table provides values for the unknown resistor R_x and the corresponding balance length l_x. A critical observation: In a meter bridge, as the unknown resistance R_x increases, the balance length l_x (measured from the end connected to R_x) should also increase. However, the provided data shows that as R_x increases, l_x decreases. This indicates an inconsistency in the experimental data or how it's presented. Given the instruction to "Plot a graph of R_x against (l-l_x)/l_x" and "Determine the slope of your graph and state its significance," it is implied that a linear relationship is expected. The standard meter bridge equation is (R_x)/(R) = (l_x)/(l-l_x), which implies R_x = R (l_x)/(l-l_x). If we plot R_x against (l-l_x)/(l_x), this would result in a curve (Y = R · X^-1). To obtain a linear graph as typically expected in such problems, we must assume the meter bridge equation is interpreted as (R_x)/(l-l_x) = (R)/(l_x), which rearranges to R_x = R ( (l-l_x)/(l_x) ). Under this assumption, plotting R_x (Y-axis) against (l-l_x)/(l_x) (X-axis) would yield a straight line passing through the origin with a slope equal to R. We will proceed with this assumption to fulfill the requirement of finding a slope. a) Find (l-l_x)/l_x. Tabulate your results. Step 1: Calculate (l-l_x) for each l_x value, where l = 1000 mm. Step 2: Calculate (l-l_x)/l_x for each pair. Convert R_x from k to . |c|c|c|c| R_x/ & l_x/mm & l-l_x/mm & (l-l_x)/l_x \\ 1000 & 840 & 1000-840=160 & (160)/(840) ≈ 0.190 \\ 1500 & 702 & 1000-702=298 & (298)/(702) ≈ 0.425 \\ 2200 & 618 & 1000-618=382 & (382)/(618) ≈ 0.618 \\ 3500 & 532 & 1000-532=468 & (468)/(532) ≈ 0.880 \\ 4500 & 456 & 1000-456=544 & (544)/(456) ≈ 1.193 \\ b) Plot a graph of R_x against (l-l_x)/l_x. To plot the graph: X-axis: (l-l_x)/l_x (dimensionless). Scale: 0 to 1.4 (e.g., 10 small squares = 0.2 units). Y-axis: R_x/. Scale: 0 to 5000 (e.g., 10 small squares = 500 ). Plot the points: (0.190, 1000) (0.425, 1500) (0.618, 2200) (0.880, 3500) (1.193, 4500) Draw the best-fit straight line* through these points. (Note: Due to the inconsistency in the provided data, the points may not fall perfectly on a straight line. A best-fit line should be drawn to represent the general trend.) c) Determine the slope of your graph and state its significance. Step 1: Choose two points on the best-fit line (not necessarily data points) that are far apart to calculate the slope. Let's pick two points from the calculated table that are roughly on the line. Using points (X_1, Y_1) = (0.425, 1500) and (X_2, Y_2) = (1.193, 4500): Slope = ( Y)/( X) = (Y_2 - Y_1)/(X_2 - X_1) Step 2: Calculate the slope. Slope = (4500 - 1500 )/(1.193 - 0.425) = (3000 )/(0.768) ≈ 3906.25 The calculated slope is approximately 3906 . This value is significantly different from the given known resistance R = 680 . This discrepancy arises from the inconsistency in the provided experimental data. However, following the assumption that R_x = R ( (l-l_x)/(l_x) ), the slope of the graph represents the known resistance R. Slope: Approximately 3906 Significance: The slope of the graph represents the value of the known resistor R. d) State two precautions you would have taken if you were to perform the experiment in a laboratory. Ensure all connections are tight* to minimize contact resistance. Avoid overheating* the wire by keeping the current on only when taking readings, to prevent changes in resistance. Use a sensitive galvanometer* to accurately detect the null point. Repeat readings and take an average* to reduce random errors. Ensure the meter rule is parallel* to the wire to avoid parallax error in length measurements. e) Explain how an ammeter is connected in an electric circuit. An ammeter is always connected in series with the component through which the current is to be measured. It has a very low internal resistance to minimize its effect on the circuit's total resistance and thus on the current being measured. Drop the next question! 📸