TFA 1043: General Physics II

E2: DC CIRCUIT ANALYSIS

OBJECTIVES

1. To practice and construct various types of circuit2. To determine the voltage, current and resistance for series, parallel and series-

parallel circuit.

APPARATUS

a) Resistors: (4 units) with different values of R,=229, R,=33O , Ra=68O and R4=100C)

b) Ammeter (1 unit)c) Alligator clip (10 units) and banana clip (6 units)d) Power Supplye) Voltmeter

THEORIES

The analysis of the DC circuits is based on the Ohm's and Kirchhoff's laws. The mainequations describing the relationship between electrical quantities such voltage, V, current, I

and resistance, R as follows:

1. Ohm's Law.

The voltage, V across a resistor is linearly dependent to the electric current, I flowing throughit. The constant of the proportionality is called the resistance, R of the resistor.

V=lR

2. Resistors in series combination (Figure 1)

The electric current, I, flowing through each of the resistor connected in series is equal to oneanother, that is,

ls=11=12=13... .=lN Q)

The voltage across the ith resistor is liRi. The totalvoltage V. is the sum of allthe voltagesacross the individual resistor in the circuit, that is,

E2

(1)

Figure 1

TFA 1043: General Physics II

V, =V, +V, +""""+Vn = IV' 'i=l

Req = 5a * Ea +........... +

Rn

I, Is I. Is

R.o R, +R, *..'.......Rn = t*,i=l

3. Resistors in parallel combination (figure 2)

El and E2

(3)

(4)

Figure 2

The voltage V, across each of resistor connected in parallel is equal to one another,

\ = vr -Yz = % :........: vN (5)

The current flowing through the ith resistor is V;/R;. The total current l. is the sum of all the

currents flowing through the individual resistor in the circuit,

N

I, = Ir +I2 + Ir +........+ I,q = I Iii=l

VVV.V^V"'s _ 's _L 5 -I 5

R.o Rl R2 R3 RN

1 I I 1 1 I''r,1

-=

T-T........-= /,-R.o Rr R2 R3 RN t:iR'

(6)

(7)

TFA 1043: General Physics II El and E2

4. The resistors in Series-parallel combination

Figure 3 shows circuits with resistors in combination of both series and parallel connections.

Figure 3

The analysis of the circuit is carried out by replacing all the resistors in series (parallel)

connection with its equivalent resistance until the final circuit only contains purely series(parallel) resistors. Once the voltage V and current I for the equivalent circuit have beendetermined, the voltage and current of the individual resistors can be determined from the V.or l, as discussed earlier.

5. Voltage Divider

From equation (3), in a circuit with two resistors in series the total voltage Vs is divided into

voltages V1 and Vo ocross each resistor.

lo

Note that the voltage Vo is the output of the voltage divider (see Figure 4) since its referencepoint is the ground. The voltage Vo c?fl be calculated as follows,

R1

R"V\r z 5

"o - B, ap,(8)

For the circuit to function as a voltage divider the output current ls may be very small relative

to the current that flows through resistor Rz.

Figure4

TFA 1043: General Physics II El andB2

PROCEDURES

1. Measure the resistance of each resistor using multimeter,

R2=-, R3=-, ?l.ld Rn=.

2. Set-up a DC circuit as shown in Figure 1 (series) and in Figure 2 (parallel) up to fourresistors (N=4) using EDISON software. With known information decide the bestvoltage and equipment that you will use.

Resistors in $eries

3. Set up manually a series circuit as in step2 (refer to figure 1). Measure and completethe table with the experimental values of the relevant circuit parameters, i.e currentl, voltage V, and resistance R.

Series Circuit

Tablel

Resistors in Parallal

4. Set up manually a parallel circuit as in step 2 (refer to figure 2). Measure and

complete the table with the experimental values of the relevant circuit parameters,

i.e current l, voltage V, and resistance R.

Figure 1

Parameters Voltaqe V) Current (A)

Vnr Vn, Vo. Vo, l*' lo, lo" In, l.EDISIONSoftware

ExperimentalValues

PercentageError

TFA 1043: General Physics II

Parallel Circuit

El andB2

Figure 2

Parameters Voltaqe V) Curren (A)

Vo. Vot Vo" Vo, V lo,' lor lo" lon

EDISIONSoftware

ExperimentalValues

PercentageError

Table 2

Resistors in Series-Parallel Combination

5. Set up manually a Series-Parallel Combination circuit as in step 2 (refer to figure 3)

Measure and complete the table with the experimental values of the relevant circuitparameters, i.e current l, voltage V, and resistance R with the nominal values of thecomponents given in Table 3. Complete the table with the theoretical values of therelevant circuit parameters.Set the voltage Vs=10 V.

Figure 3

Note: Measure the voltage V across each of the resistors and use the experimentalvalues of the resistors in combination with Ohm's law (Eqn. (1)) to determine the valueof the current I flowing through each resistor, that is, lpi i=1 ,2,3, and 4.

TFA 1043: General Physics II El andE2

Parameters Voltaqe (V) Currenl (A)

Vo. Vo, Vo, "

Vno V. lon lo" In. lno

EDISIONSoftware

ExperimentalValues

PercentageError

Table 3

6. As mentioned the above note, show clearly how you derive the values for lnr , lp2 , lp3 , lp4

and ls using mathematical calculation.

Voltage Divider

7. Set up the circuit shown in Figure 4. Complete the table below

fade4

Figure 4

Parameter Resistance (O) Voltase (V)

Rn R" V" Vn

Experimental Value

' TFA 1043: General Physics II E! andB2

TASKS:

ln this section the theoretical and experimental values will be compared. Answer the

following questions.

1. Calculate the percentage error between the theoretical (data taken from and

experimental data and complete Table 1 through 5. The percentage error is defined

as follows,

o/oerrot= dt -d" "100d,

Where dt and du are the theoretical and experimental data respectively.

2. From the results above, give your comments regarding the three parameters with the

highest percentage errors and the parameters with the lowest percentage errors.Discuss the source of these errors.

3. Referring to results in Table 3 regarding the resistance in series-parallel combination,which of the following combinations are TRUE

a. I. = I*, + IR, + I*. * Iun

b. V,b=V.-Vo"c. I, = I*-, * I.,, I*, * I**

4. Voltage divider can supply a voltage not a current at its output terminals. lf a device is

connected to the output terminal of the voltage divider, what would be the resistanceof the device?

2.5 GONCLUSION

Attach result and conclusion in your repod.

SPECIAL NOTE: (You can construct your circuit using the Breadboard. Below aresome information pertaining the used of a breadboard)

Resistor Colour Code

The value of most resistors is shown by a pattern of coloured rings. These are read starting

from the band closest to an end. The colours are internationally defined as listed below. Alas,

the precise meaning of 'red' or'blue' is not, so some variation in the actual colours used does

occur. As a result one manufacturer's brown looks like another's orange. When in doubt use

a meter to measure the value.

Remember that the colours you see here depend upon the monitor and screen mode

being displayed by your comPuter!

TFA 1043: General Physics II El andE2

Using Breadboard

A breadboard is used to make up temporary circuits for testing or to try out an idea. No

soldering is required so it is easy to change connections and replace components. Parts will

not be damaged so they will be available to re-use afteruvards.

Almost all the Electronics Club projects started life on a breadboard to check that the circuit

worked as intended.

The photograph shows a typical small breadboard which is suitable for beginners building

simple circuits with one or two lCs (chips). Larger sizes are available and you may wish to

buy one of these to start with.

Breadboards have many tinysoCkets (called'holes') arranged on a 0.1" grid. The leads of

most components can be pushed straight into the holes. lCs are inserted across the central

gap with their notch or dot to the left.

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' TFA 1043: General Physics II E1 and E2

Wire links can be made with single-core plastic-coated wire of 0.6mm diameter (the standardsize). Stranded wire is not suitable because it will crumple when pushed into a hole and itmay damage the board if strands break off.

The diagram shows how the breadboard holes are connected:

The top and bottom rows are linked horizontally allthe way across as shown by the red and

black lines on the diagram. The power supply is connected to these rows, + at the top and

0V (zero volts) at the bottom.

I suggest using the upper row of the bottom pair for 0V, then you can use the lower row forthe negative supply with circuits requiring a dual supply (e.9. *9V, 0V, -9V).

The other holes are linked vertically in blocks of 5 with no link across the centre as shownby the blue lines on the diagram. Notice how there are separate blocks of connections toeach pin of lCs.

Large BreaboardsOn larger breadboards there may be a break halflruay along the top and bottom power supplyrows. lt is a good idea to link across the gap before you start to build a circuit, otheruvise you

may forget and part of your circuit will have no power!

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