lab_electrical_engineering:1_resistors:mesh-set [MEXLE Wiki]

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====== Loop law ======

**Kirchhoff's voltage law:** In every closed loop of an electrical network, the sum of all voltages is zero.

Set the voltage on the power supply to $12 ~{\rm V}$ and measure this voltage accurately using a multimeter. Build the measurement circuit shown in <imgref Fig-2_loop-law_V1>.

{{drawio>lab_electrical_engineering:1_resistors:Fig-1_Mesh-set_V1.svg}}
<imgcaption Fig-2_loop-law_V1 | Verification of Kirchhoff's voltage law> </imgcaption>

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

{{drawio>lab_electrical_engineering:1_resistors:Table-1_Mesh-set_V1.svg}}
<tabcaption Table-4_loop-law_V1 | Voltage measurement for Kirchhoff's voltage law> </tabcaption>

What is the loop equation here?
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Verify the equation using the measured values.
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The resistors $R_{\rm 1}$ and $R_{\rm 2}$ connected in series form a voltage divider. In what ratio are the voltages $U_{\rm 1}$ and $U_{\rm 2}$?

$\frac{U_{\rm 1}}{U_{\rm 2}} =$ \\ \\ 


===== Node law ======

**Kirchhoff's current law:** At every node, the sum of all currents flowing into and out of the node is zero.

Set the voltage on the power supply to $12 ~{\rm V}$ and measure the voltage accurately using a multimeter. As a first step, build the measurement circuit shown in <imgref Fig-3_node-law-branch-currents_V1>.

{{drawio>lab_electrical_engineering:1_resistors:Fig-3_V1-Node-Set-1.svg}}
<imgcaption Fig-3_node-law-branch-currents_V1 | Branch currents for verification of Kirchhoff's current law> </imgcaption>

Add the arrows indicating the directions of currents $I_{\rm 1}$ and $I_{\rm 2}$. On both multimeters, set the DC current range and the polarity before switching on. Then measure currents $I_{\rm 1}$ and $I_{\rm 2}$ and enter the measured values in the table.

{{drawio>lab_electrical_engineering:1_resistors:Fig-4_V1-Node-Set-2.svg}}
<imgcaption Fig-4_node-law-total-current_V1 | Total current and node $K$> </imgcaption>

In what ratio are currents $I_{\rm 1}$ and $I_{\rm 2}$?

$\frac{I_{\rm 1}}{I_{\rm 2}} =$ \\ \\ 

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

{{drawio>lab_electrical_engineering:1_resistors:Table-5_Node-set_V1.svg}}
<tabcaption Table-5_node-law_V1 | Current measurement for Kirchhoff's current law> </tabcaption>

Determine the node equation for node $K$ and verify its validity.
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Using the measured values of resistors $R_{\rm 1}$, $R_{\rm 2}$ and $R_{\rm 3}$, calculate the total resistance $R_{\rm KP}$.
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Using the calculated value of $R_{\rm KP}$, verify the measured value of the total current:

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