Download Electronics Lab Intro (Lab#0) Introduction Procedure Part I. Ohm`s

Electronics Lab Intro (Lab#0)
Introduction
The main purpose of this lab is to familiarize you with some of the equipment used for
the electronics labs, while investigating Ohm’s Law and Resistive-Capacitive (RC)
circuits. Recall that Ohm’s Law states that the electrical current through a circuit
component is directly proportional to the applied bias voltage across that component:
V = I ⋅R
Equation 1
And for a uniform resistive material in a cylinder we can define resistivity, ρ, as follows:
R⋅ A
Equation 2
ρ=
L
where A is the cross-sectional area of the cylinder and L is its length.
Procedure
Part I. Ohm’s Law
A. Graphite
Measure the voltage and current with two different graphite mechanical pencil “leads”.
Increase the voltage in 0.1V steps (Do not let the current exceed 1A), and record the
corresponding current, uncertainties of voltage and current at each step. Follow the
example in page 23-26 in ROOTIntro.pdf but plot voltage (y-axis) vs current (x-axis),
compare the figure with the Ohm’s Law to see whether or not the voltage and current has
a linear relationship. If so, fit the data to a first order polynomial function, and record the
fitted resistance and its uncertainty. Measure the diameters and lengths of the two
“leads”, and calculate their resistivity and uncertainty. Show the results to TAs and
explain how you propagate the uncertainties of the resistance, diameter and length into
the resistivity uncertainty.
B. Light Bulb
Check Ohm’s Law with a light bulb. When you apply the voltage, increase it with 0.1V
steps (don’t let the current exceed 250mA), and record the corresponding current,
uncertainties of voltage and current at each step. Make plots in ROOT of the bulb
voltage (y-axis) vs current (x-axis). Does the light bulb follow Ohm’s Law? Show the
results to TAs.
Part II. RC-Circuit Time Constant
A. Charging with a constant-voltage DCpower source.
Construct the RC circuit shown in Fig. 1. Use the 5
Volt power supply. Make sure the “+” sign on the
capacitor (470µF) is oriented toward the positive side
R1
V0
+
+
Figure 1: RC-circuit.
R2
1
of the power supply. Make sure the capacitor is fully discharged initially through the
resistor R2 = 2200Ω (or 2000Ω as per availability). Start the charging process by
connecting the power supply, capacitor and resistor R1 =22kΩ (or 24kΩ as per
availability). Then the potential difference on the capacitor plates could be described as
follows:
−
t
V (t ) = V0 (1 − e τ ) ,
where
τ = R ⋅C
Equation 3
Assume t=0 to be the time at which you begin charging the capacitor. With a timer and a
DMM connected across capacitor C, measure potential difference V at intervals of 10
seconds. Make at least 6 consecutive measurements, and then wait for 2 additional
minutes before recording the final reading.
Inverting Equation 3 yields:
⎛ V ⎞
−t
ln ⎜1 − ⎟ =
⎝ V0 ⎠ R ⋅ C
Equation 4
Confirm equation 4 with the results of your measurements. Consider the final
measurement to be V0, plot the time dependence of ln(1-V/V0). Fit the data points to
extract the slope for the expected linear dependence (the slope is quantitatively -1/RC).
Compare the value with the expected value obtained from the labels on the
components. Email the figure of the fit, the expected value of RC, and the conclusion
whether they are consistent to Prof. Ye ([email protected]).
B. Charging with a Square Wave
Construct the RC circuit shown in Fig. 2.
Drive the circuit with a 500 Hz square
wave. Remember, the vertical edges of the
wave are like constant voltage sources
being switched on and off.
x
R1 =10kΩ
500 Hz
Square Wave
C=0.01uF
Oscillo
scope
Use the oscilloscope to observe the time
dependence of the output. Make a graph.
Determine the time constant of the RC
Figure 2: Square Wave Charging
circuit constructed, by measuring the time
it takes for the output to drop to 37% (1/e)
of its initial value. Cross-check your result by measuring the time needed for a rise to
63% of its final value after the polarity switch. Compare this result with the quantity RC.
Explore the effects of varying the square wave frequency on the circuit time constant.
Summarize your observations. Email Prof. Ye the graph and your observations.
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