Electrical meters
An electrical meter shows how big an electrical quantity is. The common types are:
- Ammeter (current, in amperes)
- Voltmeter (potential difference, in volts)
- Ohmmeter (resistance, in ohms) and the multimeter that does all three
- Wattmeter (power) and energy meter (units of electricity used, the meter at home)
The usual moving-coil meter has a light coil between the poles of a magnet. When current flows, the coil feels a force and turns against a spring. A needle fixed to the coil points to the scale. More current gives more turn.
How to connect them. An ammeter goes in series and must have a very small resistance, so it does not change the current. A voltmeter goes in parallel and must have a very large resistance, so it takes almost no current. To read a bigger current, put a small shunt resistor in parallel with the meter coil. To read a bigger voltage, put a large multiplier resistor in series with the coil.
Moving-coil meters work on DC only. For AC, meters use a rectifier or a moving-iron design. Digital meters show numbers on a screen.
Measurement: reading, range and error
Measuring means comparing a quantity with a standard unit and writing the number. No reading is perfect. The difference between the reading and the true value is the error.
- Range: the largest value the meter can show (full scale). Choose a range a little above the value you expect. If the needle moves less than a third of the scale, the reading is poor.
- Accuracy class: a class 1.5 meter is wrong by up to 1.5 % of full scale. On a 10 A range that is ±0.15 A at any point on the scale.
- Parallax: looking at the needle from the side gives a wrong reading. Look straight down, and use the mirror strip if the scale has one.
- Zero error: if the needle does not rest on zero, correct it first.
Sensors (also called transducers) turn a physical quantity into an electrical signal: a thermistor for temperature, a light-dependent resistor for light, a strain gauge for force, a float switch for liquid level. A meter can then read this signal.
Basics of automatic control
Automatic control means a machine keeps a value where we want it without a person watching. Words to know:
- Set value (target): what we want, for example 40 °C.
- Output (controlled variable): what we actually get, for example the room temperature.
- Sensor: measures the output.
- Controller: decides what to do.
- Actuator: does it, for example a heater, valve or motor.
- Disturbance: something that pushes the output away, like an open window.
Open loop: the controller acts without checking the output (a timer). It is simple and cheap but cannot fix errors.
Closed loop: the sensor sends the output back (feedback); the controller finds the error = set value − measured value and acts to make the error small. It can fight disturbances.
On-off control (thermostat): heater ON when too cold, OFF when warm enough. The temperature wobbles a little around the set value. Proportional control: the bigger the error, the stronger the action; it gives a smoother result.
Applications of automatic control
You will meet automatic control everywhere:
- Temperature: geyser, fridge, iron, air conditioner and oven thermostats.
- Level: a float switch starts the pump when the tank is low and stops it when full.
- Motor speed: a speed sensor on a lift or conveyor motor lets the controller keep the speed steady with a heavy or light load.
- Voltage: an automatic voltage regulator on a generator keeps the output voltage the same when the load changes.
- Safety: a circuit breaker senses over-current and cuts the supply by itself; a smoke alarm senses smoke and rings.
- Programmable controllers (PLC) and microcontrollers run factory machines with many sensors and actuators.
Good control systems are tested with a disturbance (like opening a window) to see how quickly they recover.
Try it: find the loop
Look around your home and sort things into open loop or closed loop. A fan on a timer: open. A fridge that cuts off when cold: closed. Now in the 3D: run the open-loop room, wait for the window to open, and write down the final temperature. Run the closed-loop room and compare. For measurement, draw a circuit of a battery, a bulb, an ammeter and a voltmeter, and check that the ammeter is in line and the voltmeter is across the bulb.
Key formulas and definitions
- Ammeter: connect in series, resistance very small
- Voltmeter: connect in parallel, resistance very large
- Shunt resistance S = Ig × Rg / (I − Ig)
- Multiplier resistance R = V / Ig − Rg
- Error = measured value − true value; % error = error / true value × 100
- Class error = (class / 100) × full-scale value
- Control error e = set value − measured value
Worked examples
1. A meter coil has 100 Ω and shows full scale at 1 mA. What shunt makes it a 1 A ammeter?
S = Ig Rg / (I − Ig) = 0.001 × 100 / (1 − 0.001) = 0.1 / 0.999 ≈ 0.1 Ω, joined in parallel with the coil.
2. Use the same coil (100 Ω, 1 mA) to build a 10 V voltmeter. What series resistor is needed?
Total resistance = V / Ig = 10 / 0.001 = 10000 Ω. Multiplier = 10000 − 100 = 9900 Ω.
3. An ammeter reads 4.0 A but the true current is 4.2 A. Find the percentage error.
Error = 4.0 − 4.2 = −0.2 A. % error = 0.2 / 4.2 × 100 ≈ 4.8 % (reading too low).
4. A class 1.5 ammeter has a 10 A range. What is the largest possible error in a reading?
Error = 1.5 / 100 × 10 = 0.15 A, so the reading is within ±0.15 A at any point.
5. A sensor gives 10 mV per °C. Its output is 0.37 V. What is the temperature?
0.37 V = 370 mV. Temperature = 370 / 10 = 37 °C.
6. A heater thermostat is set at 40 °C. Show what the controller does when the room is at 35 °C and at 41 °C.
At 35 °C the error = 40 − 35 = +5 °C, so the heater is ON. At 41 °C the error = −1 °C, so the heater is OFF.
7. A room loses heat at 1 unit per °C above 20 °C, and an open-loop heater gives a fixed 30 units. What steady temperature results? What if the window is opened and the loss becomes 2.5 per °C?
Steady state: heat in = heat lost. 30 = 1 × (T − 20), so T = 50 °C. With the window open: 30 = 2.5 × (T − 20), so T = 32 °C. Open loop cannot correct this fall.
Common mistakes
- Putting an ammeter in parallel across a battery or bulb. Its tiny resistance gives a huge current and can burn the meter.
- Putting a voltmeter in series. Its large resistance almost stops the current and the bulb goes out.
- Reading the needle from the side (parallax) or ignoring zero error.
- Calling a timer a closed loop. If nothing measures the result and feeds it back, it is open loop.