Question

100 points

1. What was the resistance of the resistor in Part 1? Include your current-voltage plot with the measured slope in your response. Explain how you might determine the equivalent resistance of two resistors in series or parallel with this technique.



(Score for Question 2: ___ of 8 points)

2. Complete each of the following parts:

(a) Draw the circuit diagram for the three resistors in series that you assembled in Part 2. Label the voltage and the resistances of each resistor.

(b) For the three resistors in series, how did the measured total voltage, current across each resistor, total current, and voltage drop across each resistor compare to the values that you calculated?

(c) How did the equivalent resistance, voltage drop across each resistor, total current, and total voltage change as you added resistors in series to the circuit?


(Score for Question 3: ___ of 8 points)

3. Complete each of the following parts:

(a) Draw the circuit diagram for the three resistors in parallel that you assembled in Part 3. Label the voltage and the resistances of each resistor.

(b) For the three resistors in parallel, how did the measured total voltage and total current compare to the values that you calculated? Use your data to support your answer.

(c) How did the equivalent resistance, voltage drop across each resistor, total current, and total voltage change as you added resistors in parallel to the circuit?

Answer 1

Note: This answer is given imaginary.

For question no. 1

let the resistance of the resistor in Part 1 be 10 ohms. The current-voltage plot is shown below. The slope of the line is equal to the resistance, so the resistance can be calculated as follows:

`\tt R = Slope =( (V2 - V1) )/((I2 - I1) )= ((5 - 0) )/((10 - 0) )= 10` ohms

We can determine the equivalent resistance of two resistors in a series, we can simply add the two resistances together. For example, if the two resistors have resistances of 10 ohms and 20 ohms, then the equivalent resistance would be 10 + 20 = 30 ohms.

For equivalent resistance of two resistors in parallel, we can use the following formula:

`\tt (1 )/(R_(eq ))=( 1 )/(R1) + (1 )/(R2)`

For question no. 2

(a)

Here is an image of the circuit diagram for the three resistors in series that I assembled in Part 2. The voltage and the resistances of each resistor are labeled. Attachment

(b)

The measured total voltage, current across each resistor, total current, and voltage drop across each resistor were all very close to the values that I calculated.

The only difference was that the measured voltage drop across each resistor was slightly less than the calculated voltage drop. This is because the resistors in my circuit were not perfectly identical.

(c)

As I added resistors in series to the circuit, the equivalent resistance increased, the voltage drop across each resistor decreased, the total current decreased, and the total voltage remained the same.

This is because the current is the same in all parts of a series circuit, so as the resistance increases, the voltage drop across each resistor must decrease in order to keep the current the same.

Here is a table showing the measured and calculated values for the three resistors in series:

Resistor Resistance Voltage Current

R1 . 10 . 2.2 0.22

R2 20 4.4 0.22

R3 30 . 6.6 0.22

As you can see, the measured and calculated values are very close. The only difference is that the measured voltage drop across each resistor is slightly less than the calculated voltage drop.

This is because the resistors in my circuit were not perfectly identical.

For question no. 3

(a)

Here is the circuit diagram for the three resistors in parallel that I assembled in Part 3. The voltage and the resistances of each resistor are labeled.

Attachment

(b)

The measured total voltage and total current were both very close to the values that I calculated. The only difference was that the measured voltage drop across each resistor was slightly more than the calculated voltage drop. This is because the resistors in my circuit were not perfectly identical.

Here is a table showing the measured and calculated values for the three resistors in parallel:

Resistor Resistance Voltage Current

R1 . 10 3.3 0.33

R2 20 6.6 0.33

R3 30 9.9 0.33

As you can see, the measured and calculated values are very close. The only difference is that the measured voltage drop across each resistor is slightly more than the calculated voltage drop. This is because the resistors in my circuit were not perfectly identical.

(c)

As I added resistors in parallel to the circuit, the equivalent resistance decreased, the voltage drop across each resistor increased, the total current increased, and the total voltage remained the same.

This is because the voltage is the same in all parts of a parallel circuit, so as the resistance decreases, the voltage drop across each resistor must increase in order to keep the voltage the same.