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Lab01 - Resistors

Resistance measurement

Procedure for resistance measurement:

Set the measuring device to resistance measurement
Connect the resistance to be measured to the corresponding sockets on the measuring device (the measuring device sockets labeled COM and $\Omega$
Read the measured value

There are different types of resistance measurement:

direct resistance measurement
indirect resistance measurement

Direct resistance measurement

Determine the nominal and measured values of the resistance for $R_{\rm 1}$ (brown, green, orange), $R_{\rm 2}$ (yellow, violet, red), $R_{\rm 3}$ (red, violet, red) and the incandescent lamp $R_{\rm L}$ . Also measure the approximate resistance $R_{\rm K}$ of your body from your right to your left hand.

eee1_lab:table-1_v2.png

Tab. 1: Direct resistance measurement

How do you explain the deviation between $R_{\rm L,nominal}$ and $R_{\rm L,meas}$ ?

What consequences can $R_{\rm K}$ have?

Now determine the series and parallel connections of resistors $R_{\rm 1}$ , $R_{\rm 2}$ and $R_{\rm 3}$ .
Specify the formulas used:

$R_{\rm serial}$ =

$R_{\rm parallel}$ (= $R_{\rm a}$ || $R_{\rm b}$ ) =

eee1_lab:table-2_v1-serial_parallel.png

Tab. 2: Series and parallel connections

Indirect resistance measurement

The resistances can also be determined by measuring the current/voltage.

Ohm's law: In an electrical circuit, the current increases with increasing voltage and decreases with increasing resistance.

$I=\frac{U}{R}$

Build the measuring circuit shown in figure 1 for each of the three resistors and set the voltage on the power supply to $~{\rm 12} ~{ V}$ .

Fig. 1: Indirect resistance measurement

Measure $U_{\rm n}$ [V] and $I_{\rm n}$ [mA]. Calculate $R_{\rm n}$ [k $\Omega$ ] from these values.

Tab. 3: Indirect resistance measurement

Mesh set

In every closed circuit and every mesh of the network, the sum of all voltages is zero!
Set the voltage on the power supply to $12~\rm V$ and measure this voltage precisely using a multimeter. Set up the measuring circuit shown in figure 2.

Fig. 2: Mesh-set

Add the voltage arrows and measure $U$ , $U_{\rm 1}$ und $U_{\rm 2}$ :

Tab. 4: Mesh set voltage mesurement

What is the mesh set here?

Check the formula with the measured values:

The resistors $R_{\rm 1}$ and $R_{\rm 2}$ connected in series form a voltage divider. What is the ratio between the voltages $U_{\rm 1}$ and $R_{\rm 2}$ ?

$\frac{U_1}{U_2} =$

Set of nodes

At each junction point, the sum of all incoming and outgoing currents is equal to zero!
Set the voltage on the power supply to $12~\rm V$ and measure the voltage accurately with a multimeter. In the first step, set up the measuring circuit shown in figure 3:

Fig. 3: Node-set circuit 1

Draw the arrows for the directions of currents $I_{\rm 1}$ and $I_{\rm 2}$ in figure 4. The DC current measurement range must be set on both multimeter using the rotary switch. Then measure currents $I_{\rm 1}$ and $I_{\rm 2}$ and enter the measured values in table 5.

Fig. 4: Node-set circuit 2

What is the relationship between currents $I_{\rm 1}$ and $I_{\rm 2}$ ?

$\frac{I_1}{I_2} =$

Switch the power supply back on and measure the current $I$ . Enter its value in table 5.

Tab. 5: Node set current mesurement

Determine the node set for node K and check its validity.

Using the measured values for resistors $R_{\rm 1}$ , $R_{\rm 2}$ , and $R_{\rm 3}$ , calculate the total resistance $R_{\rm KP}$ :

Using the calculated value $R_{\rm KP}$ , check the measured value of the total current:

$I=\frac{U}{R_{KP}} =$

Voltage divider as voltage source

The voltage divider shown in figure 5 is in an unloaded state, as the entire current supplied by the power supply flows through the resistors $R_{\rm 1}$ and $R_{\rm 2}$ connected in series. A resistor parallel to $R_{\rm 2}$ loads the voltage divider. Set the voltage on the power supply to $12 ~\rm V$ and measure the exact voltage with a multimeter. Set up the measuring circuit shown in figure 5. For the connected load $R_{\rm L}$ = ${\rm 10} ~{\rm k\Omega}$ , the voltage divider represents a voltage source. Like any voltage source, it has a source voltage (also called the original voltage) $U_{\rm 0}$ and an internal resistance $R_{\rm i}$ . The internal resistance of a voltage divider considered as a voltage source results from the parallel connection of the divider resistors $R_{\rm 1}$ and $R_{\rm 2}$ :

$R_i = R_1 || R_2 = \frac{R_1\cdot R_2}{R_1+R_2}$

Use the measured values of resistors $R_{\rm 1}$ and $R_{\rm 2}$ to calculate the internal resistance $R_{\rm i}$ of the voltage source:

$R_i =$

$U_0 =$

The power $P_{\rm 0}$ supplied by the power supply can be calculated using the following equation:

$P_0 = U\cdot I_1$

The power consumed by the load resistance can be determined using the following formula:

$P_L = R_L\cdot {I_2}^2$

Fig. 5: Voltage divider

Draw the equivalent voltage source of the voltage divider:

What would be the value of $U_{\rm 2}$ without $R_{\rm L}$ ?

$U_{2, zero} =$

Calculate $U_{\rm 2,L}$ and $I_{\rm 2}$ for $R_{\rm L}$ = ${\rm 10} ~{\rm k\Omega}$ using the values of the equivalent voltage source: (Provide formulas!)

$U_{2L} :$

$I_2 :$

Check the values by measuring:

$U_{2L, Meas} :$

$I_{2, Meas} :$

Check the values using Kirchhoff's rules: (Provide formulas!)

$U_{2L} :$

$I_2 :$

Nonlinear resistors

All resistors examined so far are linear resistors, for which the characteristic curve $I=f(U)$ is a straight line, s. figure 6. The resistance value of a linear resistor is independent of the current $I$ flowing through it or the applied voltage $U$ .

Fig. 6: Characteristic curve of a linear resistor

With nonlinear resistors, there is no proportionality between current and voltage. The characteristic curve of such a resistor is shown in figure 7. With these resistors, we talk about static resistance ( $R$ ) and dynamic (or differential) resistance ( $r$ ). The static resistance is determined for a specific operating point: at a specific voltage, the current is read from the resistance characteristic curve.
The calculation is performed according to Ohm's law:

$R = \frac{U}{I}$

The differential resistance around the operating point is calculated from the current difference caused by a change in the applied voltage:

$r = \frac{\Delta U}{\Delta I}$

Fig. 7: Characteristic curve of a nonlinear resistor

A light bulb is examined as an example of a nonlinear resistor. Set up the measuring circuit shown in figure 8.

Fig. 8: Measuring circuit light bulb
Set the voltage on the power supply to the voltage values from table 6. Measure the corresponding current values and enter them in table 6.

Tab. 6: Values characteristic curve light bulb

Create the characteristic curve $I = f(U)$ , s. figure 9

Fig. 9: Characteristic curve light bulb

Calculate the static resistance $R$ at the operating point $U = \rm 7.0 ~V$ :

Calculate the dynamic resistance $r$ at the operating point $U = \rm 7.0 ~V$ :

Compare the values with the values from table 1 (direct resistance measurement)

MEXLE Nuggets

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