R4 1k X A B C. R5 2k. R3 2k. R1 2k

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1 Ladder Lab Activity Studet Name: Studet Name: CICUIT SCHEMATIC Below is the circuit uder aalysis: 4 X A B C 6 4V CICUIT THEOY / CICUIT OPEATION To uderstad how this circuit works, oe must uderstad the followig: what is a ladder circuit, the eed to distiguish betwee a series coectio ad a parallel coectio i a seriesparallel circuit, ad the differet formulas ecessary to predict the operatio of the circuit. To help apprehed this, a diagram of a ladder circuit is placed below: Ladder Circuit Vs To begi with, a ladder circuit is a seriesparallel circuit which icludes both series ad parallel coectios of compoets that cotais oly two resistor values: resistors of a certai value (show as i the above diagram) ad resistors of twice that previous value (show as i the above diagram). A circuit is created i such a way that o matter what value for is used ad o matter what value the voltage source (show as Vs i the above diagram) is, the total curret i the circuit is divided i half at each juctio (poit where the circuit splits ito two paths). This pheomeo is explaied later o i this sectio. It is assumed that curret is flowig from positive () to egative () as per covetioal curret flow ad that the curret is always flowig towards the groud (show o the egative side of the voltage source).

2 Next, before performig the calculatios to predict the behavior of this circuit, oe must comprehed the differece betwee a series ad parallel coectio. The key differece betwee these two coectios is how the compoets are coected at their termials. First off, a series coectio is a oe i which two compoets are coected at oe termial oly. Cosequetly, a parallel coectio is a coectio i which two compoets are coected at both termials. Because of this differece, formulas to calculate resistace, curret, ad voltage i parallel circuits are differet tha those for series circuits. Examples of compoets i series as well as parallel coectios are show below: Compoets i Series Compoets i Parallel A ladder circuit is a seriesparallel circuit, meaig that it icludes a combiatio of both series ad parallel coectios i its circuitry although it may be difficult to perceive at first. To better see the series ad parallel coectios i a seriesparallel circuit, it is helpful redraw the circuit i questio. For example, the ladder circuit uder aalysis i this lab is show i its regular format below: 4 6 4V It is quite difficult to actually see the various series ad parallel coectios i this circuit. To help oe easily idetify the series ad parallel coectios i this circuit, the redraw model is show below: 4V

3 From this simpler redraw model, oe ca easily idetify that the oly two resistors directly i series to oe aother are 6 ad 7. That series combiatio is coected i parallel with 5. This parallel combiatio is the coected i series with 4 ad so o ad so forth. Upo differetiatig betwee a series ad parallel coectio, formulas for derivig the circuit s voltage, curret, ad resistace are used. Ulike series circuits, aalysis of parallel circuits ecompasses a totally differet midset. Although certai aspects, such as the implemetatio of Ohm s Law (which ca be used with ay type of circuit), are similar, formulas for calculatig voltage, curret, ad resistace i a parallel circuit are much differet from those of a series circuit. Furthermore, the rules of curret ad voltage for a parallel circuit are the exact opposite of those i a series circuit. I a series circuit, voltage is divided proportioally amog the various resistors of a circuit, but i a parallel circuit, it is the curret that is divided proportioally amog the resistors. This pheomeo is called the duality priciple. Coversely, although curret is the same throughout the etirety of a series circuit, it is the voltage that is uchagig throughout a parallel circuit. So, with respect to voltage ad curret, a parallel circuit is the exact opposite of a series circuit. The formulas for calculatig total resistace i a parallel circuit are show below. Whe lookig over these formulas, keep i mid that the total resistace i a series circuit is foud by simply addig up all the resistor values. Coditio Formula or more parallel resistors parallel resistors esistors of equal value T i T T i These formulas are for the most part selfexplaatory. For or more resistors i parallel, the reciprocal of the total resistace is equal to the sum of the reciprocals of the idividual resistaces i parallel. This, obviously, is more easily uderstood through the formula. The first formula for calculatig total resistace ca be very tedious ad timecosumig. Thakfully, there is aother formula for the case that there are oly two parallel resistors. This formula states that the total resistace ( T ) i a parallel circuit with two resistors is equal to the product of the two resistor values ( ) divided by the sum of those same resistor values ( ) 3

4 I the special case that all resistors i a parallel circuit are equal, a special equalvalue formula ca be used. This formula states that the total resistace is equal to the value of oe of the resistors i the parallel circuit () divided by the total umber of parallel resistors (). It is importat to remember that whe resistors are coected i parallel, the total resistace is always less tha the smallest resistor i that parallel combiatio. Fidig the total voltage i a parallel circuit is much easier tha fidig the resistace. The voltage throughout a parallel circuit remais the same for all compoets. As stated above, this is similar to curret i a series circuit. The formula below sums up this poit: V T V i Because parallel circuits divide curret proportioally like voltage i a series circuit there is a curretdivider rule (CD) for parallel circuits similar to the voltagedivider rule (VD) for series circuits show o the followig page: IT I i This formula states that the curret across a certai resistor i parallel (I i ) is equal to the product of the circuit s total curret (I T ) ad its total resistace ( T ) divided by the resistor of iterest ( i ). Furthermore, Kirchhoff s Curret Law (KCL) similar to Kirchhoff s Voltage Law (KVL) states that the sum of all the currets eterig a juctio is equal to the sum of all the currets leavig the same juctio. Kirchhoff s Curret Law is summarized below: i i T I T I i A example of Kirchhoff s Curret Law is demostrated i the diagram below: I i(a) I i(b) I A) I B) I C) I I I I I i( A) i( B) A) B) C) This diagram shows that the two currets eterig the juctio, I i(a) ad I i(b), are equal to the three currets exitig the juctio, I A), I B), ad I C). This is demostrated i the formula show below the diagram. Note that the arrow i the diagram idicates the directio i which the curret is flowig. Fially, if two of the followig is kow of a seriesparallel circuit: total curret, total voltage, or total resistace, oe ca use Ohm s Law to fid out the missig third variable. Although the above formulas ca oly be used for a parallel circuit, Ohm s Law ca be used for either a series or parallel circuit. The formulas for Ohm s Law are summarized below: 4

5 .. 3. Voltage : Curret : esistace : V I V I V I [ Volts V ] [ Amps A] [Ohms Ω] With Ohm s Law, it is imperative to remember that curret is electro flow, voltage is force that causes electro flow, ad resistace is the force that opposed electro flow. Ohm s Law demostrates the relatioship betwee voltage, curret, ad resistace. Although these ideas seem very simple, they are fudametal priciples that are very importat for this lab as well as may other labs. 3 EXPEIMENT STEPS The followig steps are performed i order to execute this experimet: ) Calculate the total resistace for this ladder circuit. ) Usig PSPICE, verify the total resistace foud i step. 3) Calculatios ecessary to predict circuit behavior are to be performed. Calculatios are performed so to fid the voltage ad curret at poits A, B, C. 4) The desigated circuit is simulated usig PSPICE. 5) Compare the calculated values with the simulatio results usig a table format. 6) Build the circuit o a protoboard. 7) Measure the voltage ad curret at poits A, B, C. 8) Compare the measured values to the calculated values ad the simulatio results usig a table format. 9) Based o your observatios, what are the voltage ad curret values at poits A, B, C if the 4 volts supply is lowered to volts? 0) Based o your observatios, what are the voltage ad curret values at poits A, B, C if the ladder is modified with Ω? Show your istructor the result for each step. 5