## PHYS 122 Introduction to DC Circuits Lab Report: Physics Answers 2021

**Question Title:**

PHYS 122 Introduction to DC Circuits Lab Report

**Full Question:**

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INTRODUCTION TO DC ELECTRIC CIRCUITS

This lab is designed to give a hands-on introduction to direct current electrical circuits using

PhET simulation. You will construct series and parallel circuits and learn to use digital meters

to measure voltage and current in a circuit and calculate resistance. The measured resistance

for series and parallel combinations of resistors will be compared with theoretical predictions.

OBJECTIVE

1. Follow circuit diagrams to construct life-like dc electric circuits using circuit elements

from a simulated tool kit and meters integral to the circuit.

2. Measure resistance of a single resistor or a combination of resistors in a circuit from direct measurements of voltage and current using a voltmeter and an ammeter.

3. Verify resistance combination rules for series and parallel circuits by comparing experimental data to theoretical prediction.

EQUIPMENT

The PhET is similar to the one used earlier: https://phet.colorado.edu/sims/html/circuitconstruction-kit-dc-virtual-lab/latest/circuit-construction-kit-dc-virtual-lab_en.html

THEORY

Ohm?s Law: The potential difference (?V) across a resistor (R) is given by ?V = IR, where I

is the current through the resistor R. This relation (Ohm?s Law) can be used to determine the

resistance of a resistor (or a combination of resisters) if the current (I) through the R is measured with an ammeter (placed in series with R) and the potential difference (?V) across them

is measured with a voltmeter (which is not integral to the circuit) as shown in Fig. 1 below.

Resistor R

Ammeter

V

Battery

Switch

Fig. 1. Arrangement for measuring resistance R of a resistor using an Ammeter (placed in series with R, as part of the circuit) and a Voltmeter (not part of the circuit).

An implementation of above schematic on the PhET simulation may look like Fig. 2 below.

Note that the resistor we chose is from the second page of the left panel of circuit elements.

Fig. 2. Circuit constructed with elements from the Virtual Lab Kit to implement the circuit

diagram in Fig. 1. The Voltmeter probes can be removed without affecting the series

circuit. The switch must be closed for current to flow through the circuit.

Resistors in Series: When two or more resistors are connected in series, the equivalent resistance of the combination is Rs:

Rs = R1 + R2 + ?..

(1)

Resistors in Parallel: When two or more resistors are connected in parallel, the equivalent

resistance of the combination is given by Rp, where

1

Rp

=

1

R1

+

1

R2

+ ?????

(2)

In analyzing the circuits, you may assume the resistance of the (ideal) voltmeter to be

infinitely large (open circuit) and the resistance of the (ideal) ammeter to be zero as

a first approximation.

2

PROCEDURE:

I. D e t er m i n i n g Resistance f r o m C u r r e nt a n d V ol t a g e Me a su r e m e n t

1. Open the Equipment link and construct the circuit in Fig. 2. Click & drag various

elements from the tool kit to the work area. Connect wires by bringing their ends

together, rotate by dragging on the end point, extend wire lengths by pulling.

Click on a joint to disconnect (using scissors). Make neat rectangular shaped circuit, with a switch to break the circuit when changes are being made.

2. Click on the resistor and the battery to set their values to 200 ? and 10.0 Volt,

respectively. Choose the battery internal resistance r = 1.00 ?. Close the switch

and read the current and voltage values from the meters. If the voltage reading is

negative, switch the voltmeter probes ? the positive (red) terminal should be connected to the higher voltage. Record values under columns ?V and I in Table 1.

3. Change the battery voltage V to values given in Table 1 and record the corresponding ?V and I values. Save a screenshot for including in the lab report.

IIa. Series C o m b i n at i on o f R e si s t o rs

1. Construct the series resistance circuit in Fig. 3 by adding to and adjusting the

circuit from part I. Since it is a single loop circuit, the Ammeter can be placed

anywhere to measure current in the loop. The resistors R 1 and R 2 should be placed

adjacent to each other between points A and B in the circuit. Click on different

circuit elements and set their values to: R 1 = 1100 ?, R 2 = 2200 ?, Battery emf

V = 10.0 volts and its internal resistance r = 1.0 ?. Close the circuit switch.

2. Take turn to place the Voltmeter probes across the resistors R 1 , R 2 , and across

points A and B (series combination R s of resistors R1 and R2) to measure the potential difference for each resistor (or their series combination). Record the

measured values in Table 2 under the column ?V (V) for rows R 1 , R 2 and R s . Also

record the current value read by the Ammeter (in Amp) for each resistor (and

their series combination under the column labeled I(A).

A

R1

R2

B

V

Ammeter

Figure 3. Series resistance circuit with imbedded Ammeter. The voltmeter is not

shown, it will be brought in to make measurement across different points.

3

IIb. Parallel Combination of Resistors

3. Construct the parallel resistance circuit shown schematically in Fig. 4. This circuit has two different current paths ? through resistors R 1 and R 2 ? so ammeters

(A 1 and A 2 ) are placed in these branches. A third ammeter (A) is placed in the

main branch to measure the current coming out of the battery before splitting off.

A physical representation of the circuit diagram may look like Fig. 5 below.

4. Click on different elements and set their values to: R 1 = 1100 ?, R 2 =2220 ?,

V= 10.0 volts, and internal resistance of the battery r = 1.0 ?. Close the switch.

5. Place the voltmeter (not shown in Fig. 4) across resistors R 1 and R 2 in turn to

measure the potential drop for each. Also measure the potential difference between points A and B across the parallel combination R p of resistors R 1 and R 2 .

Record the values in Table 3 under column ?V(V) for rows R 1 , R2 , and Rp. [Do

you expect these ?V values to be the same? Why?]

R1

Fig. 4. Circuit diagram of a parallel combination of resistors (ammeter connections shown).

A

A

A1

B

A2

R2

+

?

Figure 5. An implementation of the parallel resistance circuit in Fig. 4; a switch is

added to the main branch. The voltmeter is available for measuring ?V.

4

ANALYSIS

I. D e t er m i ni n g Resistance f r o m C u r r e nt a n d V ol t a g e Me a su r e m e n t

1. Using Ohm?s law, R = ?V/I, and the values of ?V and I from table 1, calculate R and

record in Table 1. Attach a screenshot of your circuit with meter connections shown.

II. Resistor Combinations ? Series and Parallel

2. Series Circuit: Apply Ohm?s Law to calculate the values of the resistances R 1, R2, and

Rs using measured values of ?V and I for each. Record these values to the correct number of significant figures in Table 2 under the R(?) column. Calculate the Power dissipated by each resistance using the relation P = VI for each case. Record these values

under the column labeled P(W) in the Table 2.

3. Parallel Circuit: Apply Ohm?s Law to calculate the values of the resistances R 1, R2, and

Rp (R1 and R2 in parallel) using your measured values of ?V and I for each and record

these values in Table 3 under the R(?) column. Calculate the Power dissipated by each

resistance using the relation P = VI for each case. Record these values under the column labeled P(W) in Table 3.

POST LAB QUESTIONS:

1. From your measurements of voltages and currents in the ?series circuit? you have determined R1, R2 and RS. Theory predicts that R S = R1 + R2. Calculate the percent discrepancy between the theoretical value of Rs and your experimentally determined total resistance Rs (Table 2).

2. From your measurement of voltages and currents in the ?parallel circuit? you calculated

R1, R2 and RP. Theory predicts that RP = [R1R2 / (R1+R2)]. Calculate the percent discrepancy between the theoretical value of R p and your experimentally determined total

resistance Rp.

3. Calculate the power, dissipated by each individual resistor (P1 and P2) and the one delivered by the battery (P). Based on your observations, write a general equation between P,

P1, and P2 for series and parallel configurations.

4. For the series circuit, based on your results, write an equation relating the terminal voltage of the battery (?V) to the voltages across each resistor (?V1 and ?V2).

5. For the parallel circuit, based on your results, write an equation relating the current flow

from the battery (I) to the currents flowing in each component resistor (I1 and I2).

5

LAB 5 REPORT: INTRODUCTION TO DC CIRCUITS

Partners: ______________

Name ________________

_________________________

Date: _____________

Objective:

Table 1 Determining Resistance from Measured Values of ?V and I

?V(V)

Battery emf V

(V)

10.0

R(?)

I(A)

15.0

20.0

25.0

30.0

Table 2: Series Combination of Resistors

Resistor

Measured

R1

?V (V)

I (A)

R (?)

P (W)

R2

RS

Table 3: Parallel Combination of Resistors

Resistor

Measured

R1

R2

RP

V (V)

I (A)

R (?)

P (W)

Analysis and Sample Calculation

1. R = ?V /I =

Attach a screenshot of the circuit with meter connections for resistance measurement.

2. Rs = ?V /I =

Ps = ?V x I =

3. Rp = ?V /I =

?p = ?V x I =

Post Lab Questions

1.

23

2.

3.

4.

5.

Conclusion:

24

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