Download Electrical Resistance

5. Simple Circuits
Objectives To learn how to wire up simple circuits, measure currents and voltages, verify
Ohm’s law and the formulas for equivalent resistance for series and parallel connections.
Procedure
1. Direct measurement of resistance Select resistors A and B, approximately 100Ω
and 300Ω respectively, and measure their resistance using the DMM (Digital
multimeter) functioning as an ohmmeter. Record the values as RA and RB.
2. Measurement of current and voltage You will wire up a circuit with a power
supply and a resistor, measure the current and the potential difference across the
resistor.
2.1 Draw a circuit diagram with a DC power supply connected to a resistor and an
ammeter in series. Wire up this circuit using resistor A. Set the voltage at 10.0V and
record the current.
2.2 Draw a circuit diagram with a DC power supply connected to a resistor in series with
an ammeter. Add a voltmeter connected across the resistor. Wire up this circuit using
resistor A. Set the voltage of the power supply at 10.0V and record the readings on the
ammeter and the voltmeter.
2.3 Draw a circuit diagram with a DC power supply connected to a resistor in series with
an ammeter. Add a voltmeter connected across the combination of resistor and ammeter.
Wire up this circuit using resistor A. Set the voltage of the power supply at 10.0V and
record the readings on the ammeter and the voltmeter. Compare these readings with those
in step 2.2 and give an explanation of your observation.
3. Ohm’s law You will verify Ohm’s law.
Using the wiring in step 2.3, measure both the current I and voltage V on the resistor A
for five choices of settings of the power supply so that the voltage V ranges from 0 to
10V. Record the data on a table and plot V against I . How would you verify Ohm’s law
from the graph? How would you obtain the resistance R from the graph? Finally,
compare the value of the resistance you obtain from the graph with that recorded in step
1, finding the percentage difference.
4. Resistors in series You will wire up a circuit with two resistors in series and
connected to a power supply. Determine its equivalent resistance, and verify relations
among currents and voltages.
4.1 Draw a circuit diagram with resistors A and B in series and connected to a power
supply and an ammeter. Wire up the circuit and set the voltage of the power supply at
10V. Measure (1) the currents IA through the resistor A, which is the same as IB, the
current through the resistor B; (2) the voltages VA and VB across each resistor; and (3) the
voltage VAB across both resistors.
What is the expected relation between VA, VB and VAB ? To what accuracy is this relation
verified by your data?
4.2 Calculate the effective resistance of the combination from your current and voltage
measurements using the relation Reff =VAB/IA . Compare it with what is expected from the
formula for combining resistors in series using the values RA and RB. Find the
percentage error.
5. Resistors in parallel You will wire up a circuit with two resistors in parallel and
connected to a power supply. Determine its equivalent resistance, and verify relations
among currents and voltages.
5.1 Draw a circuit diagram with resistors A in series with an ammeter and connected to a
DC power supply. Add resistor B connected across resistor A. Wire up this circuit and
measure (1) the current IAB going into the combination and (2) the voltage VA across
resistor A, which is the same as VB, the voltage across resistor B. Calculate the effective
resistance of the combination from your current and voltage measurements using the
relation Reff =VA/IAB . Compare it with what is expected from the formula for combining
resistors in parallel using the values RA and RB. Find the percentage error.
5.2 Draw a circuit diagram with resistor A in series with an ammeter and connected to a
DC power supply. Add resistor B connected across resistor A and the ammeter. Wire up
this circuit and measure the current IA through resistor A. Repeat the procedure with A
and B exchanged and measure the current IB through resistor B. What is the expected
relation between IA, IB, and IAB? To what accuracy is this relation verified by your data?
6. Power You will verify energy conservation from your data.
Calculate the powers dissipated in resistors A and B in the circuit of step 4 using the
relation P=I2R. Compare the sum of the powers with the power delivered to the
equivalent resistor, which is the product IV where I is the current flowing into the
equivalent resistor and V is the voltage across the equivalent resistor. Repeat for the
circuit of step 5. Determine in each case the accuracy with which energy conservation is
verified.