This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
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Hey talented, good to see you again. This practical is designed to help you understand Ohm's Law and how to determine resistance in different circuit configurations. Overall Objective: The experiment involves measuring current (I) and voltage (V) across different resistors or circuit setups to calculate their resistance (R) using Ohm's Law (V = IR). You'll then analyze this data graphically and solve a related problem. Part 1: Determining R₁ 1. Setup: You'll connect a circuit with a resistor (let's call it R₁), an ammeter to measure current (I₁), and a voltmeter to measure voltage (V₁) across R₁. 2. Data Collection: You'll take five sets of readings. For each set, you'll adjust the power supply to increase the current (I₁) flowing through R₁ and record the corresponding voltage (V₁) across it. 3. Calculation: For each set of readings, you'll calculate the resistance R₁ using the formula: R₁ = V₁ / I₁ (in Ohms, Ω) 4. Tabulation: Record all your I₁, V₁, and calculated R₁ values in the first table provided. Part 2: Determining R₂ 1. Setup: You'll connect a different circuit (as shown in Fig. 3.2, which isn't provided, but implies a different resistor or a combination of resistors). Let's call the resistance of this setup R₂. You'll use an ammeter to measure current (I₂) and a voltmeter to measure voltage (V₂) across R₂. 2. Data Collection: Similar to Part 1, you'll take multiple readings, increasing the current (I₂) and recording the corresponding voltage (V₂). 3. Calculation: For each set of readings, you'll calculate the resistance R₂ using the formula: R₂ = V₂ / I₂ (in Ohms, Ω) 4. Tabulation: Record all your I₂, V₂, and calculated R₂ values in the second table provided. --- Now let's look at the questions: a) Graphing V vs I You need to plot two graphs on the same graph page: 1. Graph 1: Plot the voltage V₁ (y-axis) against the current I₁ (x-axis) using the data from Part 1. 2. Graph 2: Plot the voltage V₂ (y-axis) against the current I₂ (x-axis) using the data from Part 2. Both graphs should ideally be straight lines passing through the origin, demonstrating Ohm's Law. b) Comparing Slopes and Average Resistances Step 1: Calculate the average value of R₁ from your tabulated data in Part 1. Step 2: Calculate the slope of the first graph (V₁ vs I₁). The slope of a V-I graph represents the resistance (ΔV/ΔI = R). Step 3: Compare the calculated average R₁ with the slope of the first graph. They should be very close. Step 4: Calculate the average value of R₂ from your tabulated data in Part 2. Step 5: Calculate the slope of the second graph (V₂ vs I₂). Step 6: Compare the calculated average R₂ with the slope of the second graph. They should also be very close. c) Calculating Resistor for Parallel Connection You need to find the value of a resistor (let's call it Rₓ) that, when connected in parallel with a 2 Ω resistor, results in an effective resistance (R_eff) of 1.5 Ω. Step 1: Write the formula for two resistors in parallel: 1/R_eff = 1/R₁ + 1/R₂ Step 2: Substitute the given values: 1/1.5 Ω = 1/Rₓ + 1/2 Ω Step 3: Isolate 1/Rₓ: 1/Rₓ = 1/1.5 Ω - 1/2 Ω 1/Rₓ = (2 - 1.5) / (1.5 × 2) 1/Rₓ = 0.5 / 3 1/Rₓ = 1/6 Step 4: Solve for Rₓ: Rₓ = 6 Ω The value of the resistor to be connected in parallel is 6 Ω. d) Precautions for Accurate Results Here are four precautions you could take: Ensure all connections are tight and clean* to minimize contact resistance. Read the ammeter and voltmeter scales perpendicularly* to avoid parallax error. Use a rheostat or variable power supply* to gradually change the current and voltage, taking readings at regular intervals. Allow the circuit to cool down* between readings or after prolonged use, as resistance can change with temperature. What's next? 📸