Question

Use the exact values you enter to make later calculations. Part A A group of students performed the same "Ohm's Law" experiment that you did in class. They obtained the following results: Trial ΔV (volts) I (mA) 1 1.00 4.4 2 1.90 8.4 3 3.10 13.3 4 3.90 16.8 5 5.10 22.2 where ΔV is the voltage difference across the resistor and I is the current traveling through the resistor at the same time. (a) Analyze the data. (You will not submit this spreadsheet. However, the results will be needed later in this problem.) (i) Enter the above data into an Excel spreadsheet. (ii) Make a plot of the voltage difference vs. current. Hint (iii) Use the trendline option in Excel to fit the data of voltage difference versus current to get the slope and intercept. Hint (b) Determine the slope and y-intercept of your graph, and report these values below. (Use ohm for Ω.) slope = y-intercept = Part B Your mischievous lab partner takes the resistor that you just experimented with and assembles it in a network with one other resistor and places them inside a black box. He challenges you to tell him the configuration of the resistors inside the box. Being an industrious physics student you connect the leads of the black box to your power source, voltmeter (in parallel), and ammeter (in series) and take the following simultaneous measurements. ΔV (volts) I (mA) 4.28 11.5 Use the above measurements to find the equivalent resistance of the arrangement. (Use ohm for Ω.) Req = Based on your value of the equivalent resistance, what must the arrangement be? in series in parallel Part C Now that you've answered his challenge, your lab partner asks you to give the resistance of the resistor that he added to the one you experimented with. Using the information you obtained in parts A and B, predict this value of the resistance of the second resistor.

Answer 1

A)

slope = 1/0.0044=227.27
since slope is equal to R (resistance) in Ohms law, therefore resistance = 227.27 (approximately 230 Ohms, if we find an average of the five)

Y-intercept = -0.0002

B) potential difference = 4.28 volts
current = 11.5 mA

by ohm's law V=IR, where V= potential difference, I = current, R= resistance,
therefore equivalnt resistance= V/I

R= 4.28/(11.5 * 10^-3)

= 372.17 ohms

the potential difference is 4.28, which is close to 3.9 as in the 1st case. for 3.9 volts the current was 16.8 mA, but now there has been a drop in current, which can be analyzed by a drop in voltage according to Ohm's law. Thus the circuit must have seen a rise is a resistance as is seen by the result. the initial resistance was approximately 230 ohms, but the current result gives 372 ohms. hence they must be in series.

C) in series resistance equivalent resistance is given by R= R1+R2, R1 is known to be around 230 ohms, and the total equivalent resistance in 2nd case is known to be 372 ohms. hence R2 or the added resistance = R-R1= 372-230= 142 Ohms.

so, his friend added 142 Ohms to the circuit.