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This course is designed for engineers. This subject is compiled of physical applications and concepts. This lecture includes: Measuring Instruments, Ammeter, Voltmeter, Ohmmeter, Currents and Voltages, Rc Circuits, Resistance, Galvanometer, Potential Difference, Ohm's Law
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Today’s agenda:
Measuring Instruments: ammeter, voltmeter, ohmmeter. You must be able to calculate currents and voltages in circuits that contain ―real‖ measuring instruments.
RC Circuits. You must be able to calculate currents and voltages in circuits containing both a resistor and a capacitor. You must be able to calculate the time constant of an RC circuit, or use the time constant in other calculations.
Leftovers. Optional (not for test) material, if time permits.
You know how to calculate the current in this circuit:
If you don’t know V or R, you can measure I with an ammeter.
R +r
To minimize error the ammeter resistance r should very small.
Any ammeter has a resistance r.Any ammeter has a resistance r. The current you measure is
r
r=0.5
Current with ammeter:
A
R +r +R
I = 0.285 A = 285 mA^ RA
% Error = 100
% Error = 0.3 % Not bad in a Physics 24 lab!
A Galvanometer
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/galvan.html#c
When a current is passed through a coil connected to a needle, the coil experiences a torque and deflects. See the link below for more details.
A galvanometer-based ammeter uses a galvanometer and a shunt, connected in parallel:
Everything inside the blue box is the ammeter.
The resistance of the ammeter is
A G SHUNT
G SHUNT A G SHUNT
Homework hint: ―the galvanometer reads 1A full scale‖ means a current of IG=1A produces a full-scale deflection of the galvanometer needle. The needle deflection is proportional to the current IG.
If you want the ammeter shown to read 5A full scale, then the selected RSHUNT must result in IG=1A when I=5A. In that case, what are ISHUNT and VAB (=VSHUNT)?
To achieve such a small resistance, the shunt is probably a large-diameter wire or solid piece of metal.
G A
Web links: ammeter design, ammeter impact on circuit, clamp-on ammeter (based on principles we will soon be studying).
You can measure a voltage by placing a galvanometer in parallel with the circuit component across which you wish to measure the potential difference.
r=0.5
Vab=?^ a^ b
The measurement is made with the galvanometer.
R 1 =10 k
R 2 =5 k
a (^) b
60 and 10 k resistors in parallel are equivalent to an 59.6 resistor. The total equivalent resistance is 5059.6 , so 1.19x10-3^ A of current flows from the battery.
I=1.19 mA
The voltage drop from a to b is then measured to be 6-(1.19x10-3)(5000)=0.07 V.
The percent error is.
% Error = 100 = 98% 4 Your opinions? Would you pay for this voltmeter?
To reduce the percent error, the device being used as a voltmeter must have a very large resistance, so a voltmeter can be made from galvanometer in series with a large resistance.
RSer^ RG
Everything inside the blue box is the voltmeter.
a (^) b
Vab
a (^) b
Vab
Homework hints: ―the galvanometer reads 1A full scale‖ would mean a current of IG=1A would produce a full-scale deflection of the galvanometer needle. If you want the voltmeter shown to read 10V full scale, then the selected RSer must result in IG=1A when Vab=10V.
The measurement is now made with the voltmeter.
R 1 =10 k
R 2 =5 k
RG=100 k
a (^) b
100 k and 10 k resistors in parallel are equivalent to an 9090 resistor. The total equivalent resistance is 14090 , so 4.26x10- A of current flows from the battery.
I=4.26 mA
The voltage drop from a to b is then measured to be 6-(4.26x10-3)(5000)=3.9 V.
The percent error is.
% Error = 100 = 2.5% 4 Not great, but much better. Larger Rser is needed for high accuracy.
An ohmmeter measures resistance. An ohmmeter is made from a galvanometer, a series resistance, and a battery.
RSer^ RG
The ohmmeter is connected in parallel with the unknown resistance with external power off. The ohmmeter battery causes current to flow, and Ohm’s law is used to determine the unknown resistance.
Everything inside the bluebox is the ohmmeter.
Today’s agenda:
Measuring Instruments: ammeter, voltmeter, ohmmeter. You must be able to calculate currents and voltages in circuits that contain ―real‖ measuring instruments.
RC Circuits. You must be able to calculate currents and voltages in circuits containing both a resistor and a capacitor. You must be able to calculate the time constant of an RC circuit, or use the time constant in other calculations.
Leftovers. Optional (not for test) material, if time permits.
