Day 14: Series Circuits and Resistors

Voltage

In the following experiment we set-up the required series and found in both cases that the voltage across the resistors (batteries) in series added up to the voltage of the source.  As for the current, it remained constant in each area tested.

Parallel Circuits

When we set up the bulbs in parallel currents 2 and 3 added up to current 1. The voltage in this case remained constant along each resistor (light bulb). 

Decoding and Measuring Resistors

Given the above pictured resistors we determined the coded resistance using the provided key. We then measured the true resistance and placed our results in the data table above. Our results concluded that the carbon resistor had the best result. It's discrepancy between the coded and measured resistance was less than 1%. The blue resistor that was supposed to have a much better tolerance rating in fact proved to perform much worse with a 4.76% discrepancy. Overall, the carbon resistor is a much better purchase than the blue resistor. 

The Equivalent Resistance for a Network

Given the above circuit we were asked to determine the total resistance of the system. We first calculated each section and estimated that our theoretical total resistance should be 52.17 Ω. We next set up the desired circuit as follows:

After measuring the resistance we got an experimental value of 51.9 Ω.

Applying the Loop Rule Several Times

Given the following circuit we developed 3 equations to help solve for the current across the noted resistors. Using these equations we were able to use substitution and elimination to solve for each current. 

We first substituted equation number 3 (current eq) into equation number 1 (top eq with ε1). This resulted in two equations with two unknowns (I2 and I3). Using the elimination method we solved for I3 and then plugged that back into one of the two new equations. After that we solved for I2 and then using the current equation solved for I1. However, the values shown above are incorrect after placing them in a matrix in teh calculator we doscovered that I1=1.14A, I2=0.999A, and I3=0.14A.

We next set up the circuit above onto a breadboard to verify our calculations. We measured the currents across the resistors and found the values to be extremely close to the theoretical. Our values were as follows: I1=1.151A, I2=1.005A, and I3=0.148A