Physics 184
#1 DC Circuits and Meters
Goals
By performing this lab experiment, you will:
1. learn about Ohm’s law, and about serial and parallel combinations of resistances in dc circuits,
2. better understand the properties and functionality of galvanometers,
3. learn the principles of the operation of voltmeters and ammeters in dc circuits. (Many meters now use
digital displays, but their multi-range features are similar to those we study in this lab.)
Reading:
Please read about galvanometers, ammeters, and voltmeters in Young & Freedman 12th ed. Section 26.3,
Electrical Measuring Instruments (27.4 in 9th & 10th ed.), which discusses the instruments we use and
construct in this lab experiment. Additional background is in Sections 25.1-4 and 26.1-2 (26.2-5 and
27.1-3 in 9th & 10th ed.). There are also concise chapter summaries.
The Basics
The current, I, at a point in a circuit is the charge per unit time flowing past that point. I = dQ/dt.
The potential, V, is the electric potential energy per unit of charge. V = U/q.
UNITS
Ohm’s Law states that V = IR, where I is the current through a circuit element,
I ampere (A) 1 A = 1 C/s
V is the potential difference across the circuit element, and R is the resistance
V volt (V)
1 V = 1 J/C
of the circuit element. The resistance R is the slope of the V vs. I curve.
R ohm (Ω)
1 Ω = 1 V/A
For many materials and conditions the resistance may be considered constant.
The power dissipated as heat in a resistor is P = I2R = V2/R.
DC circuits:
• The net current flowing to or from any point in a circuit is zero. (The conservation of electric charge,
as expressed in Kirchoff’s Rules).
• For two resistances in series, as in 1(a), the same current passes through each resistor, and the voltage
across each resistor is proportional to R. The equivalent resistance of the two is Req = R1 + R2.
• For two resistances in parallel, as in 1(b), the voltage across each resistor is equal, and the current
through each resistor is proportional to 1/R. The equivalent resistance is given by 1/Req = 1/R1 + 1/R2.
Apparatus
Resistors, a power supply, two digital multimeters (DVMs), a variable 0 – 999 Ω resistance box, light
bulbs, a battery, and a galvanometer (a device for observing and measuring current).
Before you Begin
• Understand the settings of your DVM: Set the DVM on a current setting
when you measure current, and on a voltage setting when you measure voltage.
An incorrect setting may destroy the DVM!
• The galvanometer is a delicate device; do not push it beyond full scale.
1(a)
Measurements
Series and Parallel Elements, Circuit 1: Use the 1.5 V battery in the circuit.
Observe the intensity of the light from the two bulbs when they are connected in
series, as in 1(a). The light intensity increases with the power dissipated in the bulb.
Explain the difference seen when the bulbs are reconnected in parallel, as in 1(b).
Galvanometer Properties, Circuits 2 &3: The galvanometer in the diagram
for Circuit 2 is represented by the dashed box containing the meter and internal
resistance Ri of the galvanometer coil. The tap, or key, switch in series with the
galvanometer protects it from large currents. Always close this switch when making
quantitative measurements, but only if the meter initially indicates low current.
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1(b)
Physics 184
A second switch is in series with the adjustable resistor box, RS.
We call these the shunt switch and shunt resistor because, when
the switch is closed, some of the current that would have gone
through the galvanometer is instead shunted through the resistor.
With the shunt switch open (circuit 2), slowly increase the dc
supply voltage until the galvanometer reads full scale (=50) with
the key switch closed. Record the current shown on the ammeter.
Now close the shunt switch (circuit 3). Leave the dc supply
voltage unchanged, and adjust the resistor box until the
galvanometer is at half-scale (=25) with the key switch closed.
Record the new ammeter current and the setting of the resistor
box. Determine the value of Ri from your data.
The internal resistance and full-scale deflection current are
important properties of a galvanometer; these will be decisive in
understanding the results from circuits 3 & 4.
4-Band Resistor Color Code
A B C
D
The colors of bands A, B, & C denote the
resistance value R according to:
R = AB x 10C,
where
Black
= 0
Brown = 1
Red
= 2
Orange = 3
Yellow = 4
Green = 5
Blue
= 6
Violet = 7
Gray
= 8
White = 9
Example
A = Red
= 2
B = Yellow = 4
C = Orange = 3
corresponds to R = 24000 Ω = 24 kΩ.
Circuit 2
Circuit 3
The color of band D denotes the tolerance
of the resistor, i.e., the accuracy of R.
Silver indicates ±10% tolerance and gold
±5% tolerance. If band D is absent the
tolerance is ±20%.
The Ammeter, Circuit 3: When the shunt switch is closed in this
circuit, the parallel combination of the shunt resistance Rs and the galvanometer effectively becomes a
working multi-range ammeter, with the scale determined by the shunt resistance.
To convert the galvanometer into a calibrated 1.0 mA–full-scale ammeter, start with the dc power supply
at low voltage and with zero shunt resistance. Gradually increase the voltage until the DVM ammeter
reads 1.0 mA.
Then increase the shunt resistance until the galvanometer reads full scale. Do not overdrive the
galvanometer. The DVM ammeter reading may have changed, so iterate until the DVM reads 1.0 mA
at the same time as the galvanometer is at full scale.
When this is done, you have successfully transformed the galvanometer and shunt resistance into a
calibrated 1.0 mA ammeter. Record the value of the shunt resistance and check out your new ammeter by
decreasing the power supply voltage to zero in 6 steps, at each point comparing the currents recorded by
the DVM ammeter and the galvanometer ammeter. Answer the questions on the report sheet.
The Voltmeter, Circuit 4: This circuit transforms the galvanometer into a
working multi-range voltmeter. Start with a large value for the adjustable
series resistor, say 900 Ω, and a small dc voltage. Increase the dc voltage
until the DVM voltmeter reads 100 mV. Now decrease the series resistance
until the galvanometer shows full scale. Iterate to satisfy both objectives
simultaneously, with the key switch closed. The galvanometer and series
resistance now constitute a calibrated 100 mV voltmeter. Record the value
of the series resistance, and check the calibration of your new voltmeter in
6 steps down to zero. Answer the questions on the report sheet.
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Circuit 4
Physics 184
Laboratory Report Sheet
#1 DC Circuits and Meters
Name: _______________________________ Partner: _____________________________
Lab Section: __________________________
Date: ____________________________
Series and Parallel Elements; Circuit 1:
Explain simply: Why does the light intensity increase when the bulbs are rewired in parallel?
Galvanometer Properties, Circuits 2 & 3:
Ammeter reading at full-scale on the galvanometer (shunt switch open):
_______________ A
Ammeter reading at half scale on the galvanometer (shunt switch closed):
_______________ A
Resistance box setting at half-scale on galvanometer:
_______________ Ω
* Internal resistance of galvanometer:
_______________ Ω
* Voltage across galvanometer with full-scale current:
_______________ V
Questions:
Why does the ammeter reading scarcely depend on whether the switch in series with Rs is open or closed?
Why does the internal resistance of the galvanometer equal Rs when the galvanometer reads half-scale?
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Physics 184
The Ammeter, Circuit 3:
Observed value of Rs needed to turn the galvanometer into a 1.0 mA ammeter: ____________ Ω
Calibration check of galvanometer ammeter: Currents in mA
1
2
3
4
5
6
DVM ammeter:
Galvanometer ammeter:
How does this data compare to the expected behavior of a 1.0 mA ammeter?
If you wanted to turn the galvanometer into a 10.0 mA ammeter, would you need a larger,
or a smaller, value of Rs? Explain.
The Voltmeter, Circuit 4
Observed series resistance needed to turn the galvanometer into a 100 mV voltmeter: __________ Ω
Calibration test of galvanometer voltmeter: Voltages in mV
1
2
3
4
5
6
DVM voltmeter:
galvanometer voltmeter:
How does this data compare to the expected behavior of a 100 mV voltmeter?
If you wanted to turn the galvanometer into a 1.0 V voltmeter, would you need a larger,
or a smaller, value for the series resistor? Explain.
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