Measurement TechniquesDC Circuits

Feb. 2009

Measurement Techniques DC Circuits Resistance (R)Ohms, , K, MVoltage (V)Volt, AC, DC, mV, KVCurrent (I)Amp, mA (milliamps), uA (microamps)

Bread Board Techniques - Series Circuits Resistance MeasurementGiven R1= 100, R2= 4.7K, R3=100K Find RTMeasurement must be made without power applied or wired to the circuit.Individual components must be removed from the circuit to measure the value accurately.

Breadboard Techniques - Series Circuit Voltage MeasurementThe voltage supplied by the (12V) voltage source is proportionally distributed across each resistor.The higher the resistor value, the greater the voltage dropKirchoffs Law The sum of the voltage drop across each resistor in the circuit will add up to the source voltage

Calculating Voltage DropsDetermine total resistance RT

Using Ohms Law calculate total current IT

Using Ohms Law again, calculate the voltage drop across R1, R2, R3RT = R1 + R2 + R3IT = Vs / RT

Bread Board Techniques - Series Circuit Current MeasurementThe meter must be configured for current measurement.The circuit must be opened and the meter placed (anywhere) in series.The same current flows from the voltage source, through the meter, each resistor, and then back to the source.

Bread Board Techniques Parallel Circuits Resistance 1 Circuit must be removed from the voltage sourceThe total resistance is less than the smallest resistor valueAvoid finger contact when measuring

Parallel CircuitsCalculating Total ResistanceR1//R2//R3 Where R1 is in parallel with R2 which is in parallel with R3

Product-Over-Sum MethodCalculate the parallel resistance of any 2 resistors at a time.First do R1//R2 using the Product-Over-Sum methodThen use the R1/2 resistance in parallel with R3

Parallel Circuits Voltage MeasurementThe source voltage (Vs) is common to all components in the circuit

Vs = VR1 = VR2 = VR3Vs

Parallel Circuits Current MeasurementI1 + I2 + I3VsR1R2R3IT = I1 + I2+ I3I2 + I3

Parallel CircuitsCurrent CalculationsTo measure current the circuit must be broken and the current meter must be placed in series with the component.

Calculating Total Current (IT)First find total resistance RTR1//R2 = (150 x 300) / (150 + 300) = 100 ohms Using Product-Over-Sum MethodRp//R3 = (100 x 100) / (100 + 100) = 50 ohms Using Reciprocal Method1/RT = 1/R1 + 1/R2 + 1/R3 = 1/150 + 1/300 + 1/100 = 0.00666 + 0.00333 + 0.01 = 0.020 RT = 1/ 0.020 = 50 ohmsNote: when the parallel resistors are equal in value, just divide by the number of Rs3K//3K = 1.5K6K//6K//6K = 2K2. Then use Ohms Law to find total current

Calculating Total Current (IT)First find total resistance RTThe power supply must be capable of supplying at least 1 amp of current2. Then use Ohms Law to find total current

50 v= -------- = 1 amp 50

Calculating Branch CurrentsITI1I3I2R1=150R2=300R3=100Vs50 V RT = 50 ohms IT = 1 ampI1 = Vs / R1 = 50/150 = 0.333333 ampsI2 = Vs / R2 = 50/300 = 0.166666 ampsI3 = Vs / R3 = 50/100 = 0.200000 amps1.00 amp

Series/Parallel CircuitsThere are multiple current paths.Resistors may be in series or parallel with other resistors.A node is where three or more paths come together.The total power is the sum of the resistors power.

Simple Combo circuitReduce the parallel connection to its series equivalent R2 // R3 = RsThen reduce the series equivalent to the total resistance as seen by the source RT = R1 + Rs

Kirchoffs says what goes out come back

Reduce & Simplify

Analysis of a combo circuitCalculate Total currentBranch currentsIR drops

Board Solution

Reduce & Simplify find RTRT = R1,2 // R3,4 = 300 // 600 = 200IT = 12 / 200 = 0.06 amps (60 mA)

Determining Total Resistance 1 1 1 1RT = R1 + R2 + R3RT = V ITRTV

Branch CurrentsIT = Ia + Ib = 40mA + 20 mA = 60 mABranch CurrentsIa = 12 / 300 = 40 mAIb = 12 / 600 = 20 mAIT Ia Ib

IR Drops (voltage across each resistor)VR1 = 40 mA x 100 = 4000 mV = 4VVR2 = 40 mA x 200 = 8000 mV = 8VVR3 = 20 mA x 200 = 4000 mV = 4VVR4 = 20 mA x 400 = 8000 mV = 8V

Bridge CircuitIn a bridge circuit the voltage difference between the two parallel branches is used to indicate the potential difference between the two points.Using the Voltage Divider FormulaVAB = VA - VB

Wheatstone Bridge null balance detectorVOUT = 0 voltsA balanced bridge can be used to measure an unknown resistance. The Wheatstone bridge can be used as an ohmmeter by comparing the unknown resistance value to a known one.

Conditioning circuit for resistive sensors and transducersThe bridge is often used as a conditioning circuit to convert the output of a resistive type sensing element into a voltage (mV)VOUT can be used to represent some type of process variable

TemperatureThermistorResistance Temperature Detectors (RTDs)PressureStrain GaugeFlow Anemometer

Kirchhoffs LawsThe algebraic sum of the voltage sources and voltage drops in a closed circuit must equal zero. This law states that the sum of the voltage drops in a series circuit must equal the applied voltage.The algebraic sum of the current entering and leaving a point must equal zero. The second law is for parallel circuits and states that the total current is the sum of all the branch currents.

When the voltage between point 1 and the negative side of the battery is equal to the voltage between point 2 and the negative side of the battery, the null detector will indicate zero and the bridge is said to be "balanced." The bridge's state of balance is solely dependent on the ratios of Ra/Rb and R1/R2, and is quite independent of the supply voltage (battery). To measure resistance with a Wheatstone bridge, an unknown resistance is connected in the place of Ra or Rb, while the other three resistors are precision devices of known value. Either of the other three resistors can be replaced or adjusted until the bridge is balanced, and when balance has been reached the unknown resistor value can be determined from the ratios of the known resistances.

Wheatstone bridges are considered a superior means of resistance measurement to the series battery-movement-resistor meter circuit discussed in the last section. Unlike that circuit, with all its nonlinearities (logarithmic scale) and associated inaccuracies, the bridge circuit is linear (the mathematics describing its operation are based on simple ratios and proportions) and quite accurate. Given standard resistances of sufficient precision and a null detector device of sufficient sensitivity, resistance measurement accuracies of at least +/- 0.05% are attainable with a Wheatstone bridge. It is the preferred method of resistance measurement in calibration laboratories due to its high accuracy.