1. After having taken the circuit measurements for Part 3, we will analyze the same

Objective:

To learn how resistors are used in series and in parallel.

To find the equivalent resistance of a circuit.

To verify Kirchhoff’s junction and loop rules

Procedures:

Experimental Data:

Results:

Part# 1 (Resistors in Series).

Data Table 1: Resistors in Series (100 Ƙ, 1 K (Ω), 2.2 K (Ω))

Battery voltage: 1.5_____V. Expected current (from V=IR): _ ____ mA

	Resistor value (Ω) color code; % variance	R value (Ω) DMM	R value (Ω) calculated from R=V/I	DMM Current, mA	DMM voltage, V	Calculated voltage, V from V=IR
R1 – 100 (Ω)	Brown, Black, Brown Gold	103	95.833	0.00048	.046	0.04944
R2 – 1k- (Ω)	Brown, Black, Red, Gold	1.015	850	0.00048	.408	0.0004872
R3 – 2.2 K- (Ω)	Red, Red, Red, Gold	2.312K	2166.66	0.00048	1.04	0.001109
Req	N.A.

Part #2 (Resistors in Parallel.)

Data Table 2: Resistors in Parallel

Battery voltage: _1.5____V

	R value (Ω) DMM	DMM Voltage, V	DMM Current, mA	Calculated Current, A from V=IR
R1 (100 Ƙ)	103	1.5	I1 =14.778	I1 =1522.134
R2 (1 K(Ω) )	1.012k	1.5	I2 =1.483	I2 =1.500796
R3 (2.2 K(Ω) )	2.3k	1.5	I3=0.668	I3=1.5364
Req	88.85	1.5	I4=17.1mA	I4=1519.335

Part 3: Resistors Combined in Series and Parallel.

PROCEDURE:

Set up the following table to record your observations. Remember to properly adjust your

DMM for each different measurement required.

Data Table 3: (Resistors in Combination)

Battery voltage: _1.5____V.

	R Value (Ƙ) DMM	DMM Voltage, V	DMM Current, A	Calculated Current, A from V=IR
R1 (100 Ƙ)	100	1.5	0.0157A	1.57
R2 (1 K- Ƙ)	1.013k	1.5	0.00154	1.56
R3 (2.2 K- Ƙ)	2.2k	1.5	0.00065	1.43
R2 + R3 Parallel	956.52	1.5	0.001565	1.49
Rtotal	103.213	1.5
Req	1056.52	1.5	0.0015	1.584

Part 4: Testing Kirchhoff’s Rules.

1. After having taken the circuit measurements for Part 3, we will analyze the same

circuit using Kirchhoff’s rules.

2. Check Kirchhoff’s first rule for junction DF. Remember to treat the currents flowing

into the junction as positive and the currents coming out of the junction as negative.

3. Do your measured currents for junction DF add up to zero?

4. Test the Kirchhoff’s second rule for the marked loop.

5. Do your voltages measured around the indicated loop add up to zero?

Discussion/ Analysis:

Now using the Ohm’s Law equation V = IR, calculate the expected values of the currents and voltages of all resistors tested above. Create new tables for these results. Use only the voltage supplied by the 1.5-V battery and the resistance values for the three resistors. When using the current in calculations (V = IR), you must convert mA to A by dividing the mA value by 1000. For example, in a circuit with a 1.5-V battery and a 500 Ƙ resistor, what is the expected current?

Series Resistors: Req = R1 + R2 + R3. First, find the equivalent resistance Req for all resistors involved. Then find the current through Req. The voltage for each resistor can be calculated using the resistor value, current and the equation V=IR.

Parallel Resistors:  This method of calculation can be used for calculating any number of individual resistances connected together within a single parallel network. If there are only two individual resistors in parallel then a simpler and quicker formula can be used to find the total resistance value, and this is given as:

Using the measured voltage, calculate the currents for each resistor. The total circuit current, I, is simply the sum of the currents through each resistor I1, I2, and I3.

Combination: First, find the equivalent resistance R23 of the parallel resistors, then the equivalent resistance Req for the entire circuit. Next, find the current through Req, and this should be the current through R1 and R23. Using that current, find voltages across R1 and R23.Then you can find the current through R2 and R3.

 

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