Measurement Techniques

1. Measurement Techniques DC Circuits Feb. 2009

2. Measurement Techniques DC Circuits • Resistance (R) • Ohms, Ω, KΩ, MΩ • Voltage (V) • Volt, AC, DC, mV, KV • Current (I) • Amp, mA (milliamps), uA (microamps)

3. Series Circuit RT = R1 + R2 + R3 RTΩ RT R1 R2 R3 Bread Board Techniques - Series Circuits Resistance Measurement • Measurement must be made without power applied or wired to the circuit. • Individual components must be removed from the circuit to measure the value accurately. Given R1= 100, R2= 4.7K, R3=100K Find RT

4. Vs 12V VR1 R1 R2 R3 Vs VR2 VR3 Vs = VR1 + VR2 + VR3 Breadboard Techniques - Series Circuit Voltage Measurement • The voltage supplied by the (12V) voltage source is proportionally distributed across each resistor. • The higher the resistor value, the greater the voltage drop • Kirchoffs Law – The sum of the voltage drop across each resistor in the circuit will add up to the source voltage

5. Vs 12V IT VR1 R1 R2 R3 Vs VR2 VR3 VR1 = IT x R1 VR2 = IT x R2 VR3 = IT x R3 Calculating Voltage Drops RT = R1 + R2 + R3 • Determine total resistance RT • Using Ohms Law calculate total current IT • Using Ohms Law again, calculate the voltage drop across R1, R2, R3 IT = Vs / RT

6. IR1 IT R1 R2 R3 Vs Vs 12V IR2 IT IT IT IR3 IT = IR1 = IR2 = IR3 IT Bread Board Techniques - Series Circuit Current Measurement • The 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.

7. RTΩ RT R1 R2 R3 Bread Board Techniques – Parallel CircuitsResistance • Circuit must be removed from the voltage source • The total resistance is “less than” the smallest resistor value • Avoid finger contact when measuring 1

8. 1 1 1 1 RTΩ Parallel Circuit RT R1 + R2 + R3 = RT R1 R2 R3 Parallel CircuitsCalculating Total Resistance R1//R2//R3 Where R1 is in parallel with R2 which is in parallel with R3

9. Let Rp = R1 // R2 R1 x R2 R1 + R2 Rp = R1 R2 R3 Now RT = Rp // R3 RT Rp x R3 Rp + R3 RT = Product-Over-Sum Method • Calculate the parallel resistance of any 2 resistors at a time. • First do R1//R2 using the Product-Over-Sum method • Then use the R1/2 resistance in parallel with R3

10. R1 R2 R3 Parallel Circuits Voltage Measurement The source voltage (Vs) is common to all components in the circuit Vs = VR1 = VR2 = VR3 Vs

11. I1 I2 I3 IT Parallel Circuits Current Measurement I1 + I2 + I3 Vs R1 R2 R3 I2 + I3 IT= I1 + I2+ I3

12. IT I1 I2 I3 Vs R1 R 2 R3 Parallel CircuitsCurrent Calculations To measure current the circuit must be broken and the current meter must be placed in series with the component.

13. Vs 50V R1 150 Ω R2 300 Ω R3 100 Ω Calculating Total Current (IT) • First find total resistance RT 2. Then use Ohm’s Law to find total current Using Product-Over-Sum Method R1//R2 = (150 x 300) / (150 + 300) = 100 ohms Rp//R3 = (100 x 100) / (100 + 100) = 50 ohms Note: when the parallel resistors are equal in value, just divide by the number of R’s 3K//3K = 1.5K 6K//6K//6K = 2K Using Reciprocal Method 1/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 ohms

14. Vs 50V R1 150 Ω R2 300 Ω R3 100 Ω Total Current IT Vs RT IT = Calculating Total Current (IT) • First find total resistance RT 2. Then use Ohm’s Law to find total current 50 v = -------- = 1 amp 50 Ω The power supply must be capable of supplying at least 1 amp of current

15. Calculating Branch Currents RT = 50 ohms IT = 1 amp IT I1 I2 I3 Vs 50 V R1=150 R2=300 R3=100 I1 = Vs / R1 = 50/150 = 0.333333 amps I2 = Vs / R2 = 50/300 = 0.166666 amps I3 = Vs / R3 = 50/100 = 0.200000 amps 1.00 amp

16. Series/Parallel Circuits • There 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.

17. --/\/\/\/\-- Rs I R E Simple Combo circuit Reduce the parallel connection to its series equivalent R2 // R3 = Rs Then reduce the series equivalent to the total resistance as seen by the source RT = R1 + Rs

18. Kirchoff’s says “what goes out come back”

19. R1 R3 R2 R4 R1 R3 + + R2 R4 RT = R1,2 // R3,4 Reduce & Simplify

20. 100 200 200 400 12 V Analysis of a combo circuit • Calculate • Total current • Branch currents • IR drops Board Solution

21. 100 200 200 400 300 600 12 V 12 V 200 Ώ Reduce & Simplify – find RT RT = R1,2 // R3,4 = 300 // 600 = 200 IT = 12 / 200 = 0.06 amps (60 mA)

22. R1 R2 R3 R1 R2 R3 RT IT Determining Total Resistance 1 1 1 1 RT = R1 + R2 + R3 V RT RT = V IT

23. 100 200 200 400 300 600 12 V Branch Currents IT Ia Ib Branch Currents Ia = 12 / 300 = 40 mA Ib = 12 / 600 = 20 mA IT = Ia + Ib = 40mA + 20 mA = 60 mA

24. 60 mA 40 mA 20 mA R1 R3 100 200 R2 R4 200 400 12 V IR Drops (voltage across each resistor) VR1 = 40 mA x 100 = 4000 mV = 4V VR2 = 40 mA x 200 = 8000 mV = 8V VR3 = 20 mA x 200 = 4000 mV = 4V VR4 = 20 mA x 400 = 8000 mV = 8V

25. VA = R2 x Vs R2 + R1 VB = R4 x Vs R4 + R3 R1 R3 R2 R4 AB Vs VAB VA VB Bridge Circuit In a bridge circuit the voltage difference between the two parallel branches is used to indicate the potential difference between the two points. VAB = VA - VB Using the Voltage Divider Formula

26. Wheatstone Bridge – null balance detector VOUT = 0 volts A 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.

27. R1 R1 VOUT A B Vs R1 Rs Conditioning circuit for resistive sensors and transducers • VOUT can be used to represent some type of process variable • Temperature • Thermistor • Resistance Temperature Detectors (RTD’s) • Pressure • Strain Gauge • Flow • Anemometer The bridge is often used as a conditioning circuit to convert the output of aresistivetype sensing element into a voltage (mV)