### Purpose

To determine the mathematical relationship between current, potential difference, and resistance in a simple circuit, and also to compare the potential versus current behavior of a resistor to that that of a light bulb.

### Hypothesis

The graph of potential difference versus current for a resistor should result in a linear plot, in accordance with the equation R = V / I. To extract even more from this equation, the slope of said linear plot will be equal to the resistance. The potential versus current behavior for that of a light bulb is predicted to not follow Ohm’s law, as light bulbs give off heat and light. It is not expected to have the same linear plot of current versus time that a resistor is characteristic of.

### Labeled Diagrams

See attached sheet.

### Data

Slope of regression line (V/A) | y-intercept of regression line (V) | |

Resistor 10 Ω | 9.655 | 0.0004256 |

Resistor 51 Ω | 48.94 | -0.009978 |

Light bulb (first 3 points) | 3.261 | 0.001954 |

Light bulb (last 10 points) | 37.66 | -2.248 |

### Graphs

**Resistor 10 Ω**

**Resistor 51 Ω**

**Light Bulb First 3 Points**

**Light Bulb Last 10 Points**

### Questions

**1. As the potential across the resistor increased, the current through the resistor increased. If the change in current is proportional to voltage, the data should be in a straight line and it should go through zero. In these two examples how close is the y-intercept to zero? Is there a proportional relationship between voltage and current? If so, write the equation for each run in the form potential = constant x current. (Use a numerical value for the constant.)**

The y-intercept is extremely close to zero for both the 10 Ω and 51 Ω resistor, being 0.0004256 V and -0.009978 V respectively. Yes, there is a proportional relationship between voltage and current. The equation for the first run (10 Ω resistor) is U = 9.655 I and the equation for the second run (51 Ω resistor) is U = 48.94 I.

**2. Compare the constant in each of the above equations to the resistance of each resistor.**

The constants are nearly equal to the resistance of their respective resistor.

**3. The constant you determined in each equation should be similar to the resistance of each resistor. However, resistors are manufactured such that their actual value is within a tolerance. For most resistors used in this lab, the tolerance is 5% or 10%. Check with your instructor to determine the tolerance of the resistors you are using. Calculate the range of values for each resistor. Does the constant in each equation fit within the appropriate range of values for each resistor?**

The range for the 10 Ω resistor is 9.5 Ω to 10.5 Ω. The determined constant of 9.655 fits into this range. The 51 Ω resistor has a range of 48.45 Ω and 53.55 Ω. The determined constant of 48.94 fits within that range.

**4. Do your resistors follow Ohm’s law? Base your answer on your experimental data.**

Yes, they follow Ohm’s law because the correlation for linear fit for each trial is equal to 1.000.

**5. Describe what happened to the current through the light bulb as the potential increased. Was the change linear? Since the slope of the linear regression line is a measure of resistance, describe what happened to the resistance as the voltage increased. Since the bulb gets brighter as it gets hotter, how does the resistance vary with temperature?**

The change was more curved at low voltage, but became more linear as the voltage was raised higher. Resistance increased as the voltage increased, as the slope was 3.261 V/A for the first 3 points and 37.66 V/A for the last 10 points. Since the bulb gets brighter as it gets hotter, that means resistance increases with temperature.

**6. Does your light bulb follow Ohm’s law? Base your answer on your experimental data.**

The light bulb seemed to follow Ohm’s law for the first few points, but the data began to curve into a steeper linear plot as voltage was increased. This is evident by the change in slop from 3.261 V/A for the first 3 points and 37.66 V/A for the last 10 points. The y-intercept for the last 10 points is also non-zero, which goes against Ohm’s law.