**Experiment 2: Introduction to Circuits**

In this lab, you will gain some experience using two basic electronic instruments: a DC power supply, which produces an adjustable DC voltage, and a digital multimeter, which can measure resistance and voltage. You will construct some simple circuits using resistors and light bulbs and make measurements to check the validity of Kirchhoff's Rules.

Let us review some of the fundamentals of electric circuits. The resistance R of a circuit element is defined as the ratio of the voltage drop across the element to the current flowing through it,

(1)

If the resistor is *ohmic,* then the ratio V/I is a constant, independent
of current or voltage, and the resistance is constant. However, many materials,
such as light bulb filaments, are non-ohmic; their resistance depends on
the applied current and voltage. When a light bulb filament is glowing
white hot, its resistance is much greater than when it is cool.

Resistors can be combined in *series* or in *parallel*. The
total resistance of several resistors in series is just the sum of the
individual resistances. Note that the total series resistance is always
__larger__ than any of the individual resistances.

(2) (series)

The total resistance of several resistors in parallel is always __smaller__
than any of the individual resistances according to the formula:

(3) (parallel)

In the case of two resistors in parallel, equation (3) becomes:

(4) (parallel).

__Kirchhoff's junction rule__ states that, in steady state, the sum
of the currents flowing into a junction must be equal to the total current
flowing out of the junction (otherwise charge would be building up at the
junction, and we would not be in steady state.) In the example shown here,
there are two currents I_{1} and I_{2} shown flowing into
a junction and one current I_{3} is coming out. The junction rule
says that .

Kirchhoff's loop rule states that, in traversing any closed loop in
a circuit, the sum of the voltage rises must equal the sum of the voltage
drops. You can think of voltage as a kind of electrical pressure. Voltage
differences push charges through an electrical conductor, just as pressure
differences push water through a pipe. Water in a pipe always flows from
regions of high pressure to regions of low pressure, except in a *pump,*
which forces the water to flow toward high pressure. Likewise in a circuit,
(positive) charges flow from high voltage to low voltage, except within
a battery or power supply, which forces the charges "upstream"
toward higher voltage. The voltage at a point in an electrical circuit,
like the pressure at a point in a network of pipes, has a constant, well-defined
value. If we traverse any closed loop in a circuit, or in a network of
pipes, we must return to our original voltage (or pressure). Thus the total
voltage(pressure) drop must just equal the total voltage (pressure) rise.

The two instruments you will use in this lab are a DC power supply and a digital multimeter. The DC power supply produces a constant voltage, which can be adjusted from between zero and 30 volts with the voltage knob on the front panel. The power supply has three output terminals: plus (red), minus (black), and ground (green). The ground terminal is always at zero volts. In this experiment, the ground and minus terminals are tied together by a metal connector so the minus terminal is also at zero volts. Both the current and voltage produced by the power supply can be read on meters on the front panel. Also on the front panel is a current-limit knob, which can be adjusted to limit the maximum output current, to prevent damage to sensitive circuit elements. In this lab, the current knob has been set and clamped in place so the power supply cannot produce more than about 0.6A current.

The hand-held digital multimeter (DMM)is a wonderful little device which can be used to measure voltage and current (DC or AC), resistance, and capacitance. In this lab, we will use it to measure resistance and DC voltage only. When making any measurement, there are always 2 wires to the DMM. One of the two wires always goes to the COM (common) terminal. To measure voltage or resistance, the second wire is attached to the VW input. In this lab, all our measurements will be DC, so the DC/AC switch (upper right) should always be in the DC position. The DMM has an alarm; it sings if you have wires plugged into positions which conflict with the central knob’s position. (For instance, if you have the wires in COM and VW , but have the center knob in the "Amps" quadrant.)

The DMM has two special cables called "needle probes" - long wires with pointed metal ends. You can quickly measure the voltage between any two points in a circuit by touching the points with the needle probes.

When measuring a resistance with a DMM, you must disconnect the source of the resistance (be it single resistor or some combination of resistors) from any other devices, such as power supplies. Never try to measure the resistance of a resistor while it is in a circuit.

**Procedure**

__Part I. Measurement of resistance__

Each position
should have 5 resistors: one 15W , one 40W
, one 1500W , and two 3000W
resistors. These values for the resistances are given by the manufacturer
and are *approximate*. Each resistor is mounted in a double-banana
plug connector. Begin by carefully measuring the resistance of each resistor
with your DMM and record your measured resistances. The double-banana mount
can be plugged directly into the DMM, without using any wires.

There are also two light bulbs at each position. Use the DMM with the needle probes to measure the resistance of each light bulb filament. Remember to always record your measurements directly in your lab book in ink.

Take the three large-valued resistors (the 1500W
and the two 3000W resistors) and place all three
in parallel, by stacking the double-banana plugs as shown in the diagram.
Now use the DMM to measure the total resistance of this parallel combination
of three resistors*.* Compare your measured R_{total} with
the value you expect from your earlier measurement of the individual resistances
and equation(3).

Repeat this procedure for some other combination of resistors in parallel and some other combination of resistors in series.

Use the DMM with needle probes to measure the resistance of your body
between your right and left hands. Measure the resistance by holding the
probes tightly with *dry* hands. Then wet your fingers and repeat
the measurement. You will find that wet skin has a much lower resistance
than dry skin. (Stabbing each hand with a probe would result in an even
smaller resistance, but this procedure is not recommended.)

__Part 2. The resistance of a hot light bulb filament.__

Using connecting wires and the "plug board", build a circuit consisting of the DC power supply in series with the 15W resistor and one light bulb. Whenever you build any circuit with a variable voltage source, you should always make certain that the voltage is turned down to zero (fully CCW) before connecting any wires.

Slowly, turn up the voltage until the bulb begins to glow brightly (not
too bright, we want the bulbs to last!). Now using the DMM with needle
probes, measure the voltage V across the power supply terminals, the voltage
V_{R} across the 15W resistor and the
voltage V_{B} across the light bulb. Using the known resistance
of the resistor (measured in Part I), compute the current I_{R},
though the resistor. The current though the light bulb I_{B} is
equal to I_{R}, since the resistor and bulb are in series. From
these measurements, you can compute R_{B}, the resistance of the
bulb. Compare with the value you measured in Part I. Why are they different?

__Part 3. Qualitative investigation of circuit behavior.__

Construct the circuit shown below, consisting of two light bulbs in series with the power supply. (The resistor R will be added later). Slowly increase the voltage until the bulbs are glowing (not too bright!). Now place the R = 40W resistor in parallel with bulb 2 as shown. What happens to the brightness of the two bulbs? Explain.

Repeat this procedure with R = 1500W and R = 15W . What happens in each case? Explain.

__Part 4. Kirchhoff's Laws.__

Construct the following circuit (Remember to keep the voltage turned down to zero, initially!). Increase the power supply voltage to about 10V. Now measure the voltage across the power supply terminals and across each resistor. From your measured voltages and the resistances you measured in Part 1, compute the current through each resistor. Use your measured voltages and computed currents to verify Kirchhoff's loop rule and current rule.

** **

**Prelab questions.**

**1. **Suppose the resistance of your body between your right and
left hands is R_{body}=500kW . What
would be the current through your body if you touched the plus and minus
terminals of the power supply used in this lab, with the voltage knob on
the supply is turned all the way up? The threshold of sensation for electric
current through your body is about 300m A. Would
you feel the current?

**2. **Suppose all 5 resistors used in this lab were placed in parallel.
What would be the total equivalent parallel resistance? What would be the
total resistance if all 5 resistors were placed in series.

**3. **Make a sketch to show how you would use the DMM with needle
probes to measure the power supply voltage in the circuit used in Part
2 of this lab.

**4.** For the circuit in Part 4, is the current through the 1500W
greater than, less than, or equal to the current through one of the 3000W
resistors.

**5.** Make a sketch to show how you would connect two light bulbs
*in parallel* to the power supply .