Transcript Slide 1
Measurement Techniques DC Circuits Feb. 2009 Measurement Techniques DC Circuits • Resistance (R) – Ohms, Ω, KΩ, MΩ • Voltage (V) – Volt, AC, DC, mV, KV • Current (I) – Amp, mA (milliamps), uA (microamps) 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. RT Ω Series Circuit RT = R1 + R2 + R3 RT R1 R2 R3 Given R1= 100, R2= 4.7K, R3=100K Find RT 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 Vs VR1 12V R1 Vs R2 R3 VR3 Vs = VR1 + VR2 + VR3 VR2 Calculating Voltage Drops 1. Determine total resistance RT RT = R1 + R2 + R3 2. Using Ohms Law calculate total current IT IT = Vs / RT 3. Using Ohms Law again, calculate the voltage drop across R1, R2, R3 VR1 IT Vs 12V R1 Vs R2 R3 VR3 VR1 = IT x R1 VR2 = IT x R2 VR3 = IT x R3 VR2 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. IR1 IT R1 IT Vs IT Vs IT 12V IT R2 R3 IR3 IT = IR1 = IR2 = IR3 IR2 Bread Board Techniques – Parallel Circuits Resistance • Circuit must be removed from the voltage source • The total resistance is “less than” the smallest resistor value • Avoid finger contact when measuring 1 RT Ω RT R1 R2 R3 Parallel Circuits Calculating Total Resistance RT Ω Parallel Circuit 1 1 1 1 = RT RT R1 R1 + R2 + R3 R2 R3 R1//R2//R3 Where R1 is in parallel with R2 which is in parallel with R3 R1 R2 RT Let Rp = R1 // R2 Rp = R1 x R2 R1 + R2 Now RT = Rp // R3 RT = Rp x R3 Rp + R3 R3 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 Parallel Circuits Voltage Measurement The source voltage (Vs) is common to all components in the circuit Vs = VR1 = VR2 = VR3 Vs R1 R2 R3 Parallel Circuits Current Measurement IT I1 Vs R1 I1 + I2 + I3 I2 R2 I2 + I3 IT = I1 + I2+ I3 I3 R3 Parallel Circuits Current Calculations To measure current the circuit must be broken and the current meter must be placed in series with the component. IT Vs I1 I2 R1 I3 R2 R3 Calculating Total Current (IT) Vs 50V R1 150 Ω R2 300 Ω R3 100 Ω 1. 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 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 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 Calculating Total Current (IT) Vs 50V R1 150 Ω R2 300 Ω R3 100 Ω 1. First find total resistance RT 2. Then use Ohm’s Law to find total current Total Current IT IT = Vs RT 50 v = -------- = 1 amp 50 Ω The power supply must be capable of supplying at least 1 amp of current Calculating Branch Currents RT = 50 ohms IT = 1 amp IT I1 I2 I3 Vs 50 V R1=150 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 R2=300 R3=100 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. 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 --/\/\/\/\-Rs RT = R1 + Rs I E R Kirchoff’s says “what goes out come back” Reduce & Simplify R1 R2 R3 R4 RT = R1,2 // R3,4 R1 R3 + + R2 R4 Analysis of a combo circuit 100 200 200 400 12 V Board Solution Calculate 1. Total current 2. Branch currents 3. IR drops Reduce & Simplify – find RT 100 200 300 12 V 200 600 400 RT = R1,2 // R3,4 = 300 // 600 = 200 12 V 200 Ώ IT = 12 / 200 = 0.06 amps (60 mA) Determining Total Resistance IT R1 R2 R3 V RT RT = V IT R1 RT R2 R3 1 1 1 1 RT = R1 + R2 + R3 Branch Currents IT 100 Ia Ib 200 300 12 V 200 400 Branch Currents Ia = 12 / 300 = 40 mA Ib = 12 / 600 = 20 mA IT = Ia + Ib = 40mA + 20 mA = 60 mA 600 IR Drops (voltage across each resistor) 60 mA 40 mA 20 mA VR1 = 40 mA x 100 = 4000 mV = 4V 12 V R1 R3 100 200 R2 R4 VR3 = 20 mA x 200 = 4000 mV = 4V 200 400 VR4 = 20 mA x 400 = 8000 mV = 8V VR2 = 40 mA x 200 = 8000 mV = 8V 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 VAB = VA - VB R1 A Vs VA R2 Using the Voltage Divider Formula R3 B R4 VA = VB R2 x Vs R2 + R1 VB = R4 x Vs R4 + R3 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. Conditioning circuit for resistive sensors and transducers R1 Vs A R1 R1 VOUT B Rs 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 a resistive type sensing element into a voltage (mV)