Section 2

Resistive networks

viz

V_o=V_i\frac{R_2}{R_1+R_2}

Shows Vo vs R2 on the unloaded voltage divider: Vo is the fraction R2/(R1+R2) of Vi.

Linear resistive DC network; unloaded divider unless RL is stated.

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Current divider

viz

I_1=I_T\frac{R_2}{R_1+R_2}

Splits the total current between branches: I1 = IT R2/(R1+R2).

Linear resistive DC network; unloaded divider unless RL is stated.

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Loaded voltage divider

viz

V_o=V_i\frac{R_2\parallel R_L}{R_1+(R_2\parallel R_L)}

Load RL in parallel with R2 lowers Vo versus the unloaded divider.

Linear resistive DC network; unloaded divider unless RL is stated.

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Wheatstone bridge

V_o=V_s\left(\frac{R_2}{R_1+R_2}-\frac{R_4}{R_3+R_4}\right)

Computes Wheatstone bridge from the circuit model and the stated conditions.

Linear resistive DC network; unloaded divider unless RL is stated.

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Wheatstone bridge balance

\frac{R_1}{R_2}=\frac{R_3}{R_4}

Computes Wheatstone bridge balance from the circuit model and the stated conditions.

Linear resistive DC network; unloaded divider unless RL is stated.

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Thévenin voltage

viz

V_{\mathrm{Th}}=V_{\mathrm{oc}}

VTh is the open-circuit voltage of the Thévenin equivalent that replaces the network.

Linear resistive DC network; unloaded divider unless RL is stated.

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Thévenin resistance

viz

R_{\mathrm{Th}}=\frac{V_{\mathrm{prueba}}}{I_{\mathrm{prueba}}}

RTh is the resistance seen at the terminals with independent sources killed.

Linear resistive DC network; unloaded divider unless RL is stated.

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Norton current

viz

I_N=I_{\mathrm{sc}}

IN is the short-circuit current of the Norton equivalent.

Linear resistive DC network; unloaded divider unless RL is stated.

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Norton resistance

viz

R_N=R_{\mathrm{Th}}

RN equals RTh: the same resistance in the Norton equivalent.

Linear resistive DC network; unloaded divider unless RL is stated.

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Thévenin–Norton equivalence

viz

V_{\mathrm{Th}}=I_NR_N

The equivalents satisfy VTh = IN RN and swap without changing Vo on RL.

Linear resistive DC network; unloaded divider unless RL is stated.

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Maximum power transfer

R_L=R_{\mathrm{Th}},\qquad P_{\max}=\frac{V_{\mathrm{Th}}^2}{4R_{\mathrm{Th}}}

Computes Maximum power transfer from the circuit model and the stated conditions.

Linear resistive DC network; unloaded divider unless RL is stated.

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Superposition principle

x=\sum_k x_k

Computes Superposition principle from the circuit model and the stated conditions.

Linear resistive DC network; unloaded divider unless RL is stated.

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Nodal analysis with KCL

\sum_k\frac{V_n-V_k}{R_{nk}}=I_n

Computes Nodal analysis with KCL from the circuit model and the stated conditions.

Linear resistive DC network; unloaded divider unless RL is stated.

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Mesh analysis with KVL

\mathbf{R}\mathbf{I}=\mathbf{V}

Computes Mesh analysis with KVL from the circuit model and the stated conditions.

Linear resistive DC network; unloaded divider unless RL is stated.

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Section 2

Resistive networks

Voltage divider

viz

V_o=V_i\frac{R_2}{R_1+R_2}

Shows Vo vs R2 on the unloaded voltage divider: Vo is the fraction R2/(R1+R2) of Vi.

Linear resistive DC network; unloaded divider unless RL is stated.

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Current divider

viz

I_1=I_T\frac{R_2}{R_1+R_2}

Splits the total current between branches: I1 = IT R2/(R1+R2).

Linear resistive DC network; unloaded divider unless RL is stated.

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Loaded voltage divider

viz

V_o=V_i\frac{R_2\parallel R_L}{R_1+(R_2\parallel R_L)}

Load RL in parallel with R2 lowers Vo versus the unloaded divider.

Linear resistive DC network; unloaded divider unless RL is stated.

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Wheatstone bridge

V_o=V_s\left(\frac{R_2}{R_1+R_2}-\frac{R_4}{R_3+R_4}\right)

Computes Wheatstone bridge from the circuit model and the stated conditions.

Linear resistive DC network; unloaded divider unless RL is stated.

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Wheatstone bridge balance

\frac{R_1}{R_2}=\frac{R_3}{R_4}

Computes Wheatstone bridge balance from the circuit model and the stated conditions.

Linear resistive DC network; unloaded divider unless RL is stated.

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Thévenin voltage

viz

V_{\mathrm{Th}}=V_{\mathrm{oc}}

VTh is the open-circuit voltage of the Thévenin equivalent that replaces the network.

Linear resistive DC network; unloaded divider unless RL is stated.

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Thévenin resistance

viz

R_{\mathrm{Th}}=\frac{V_{\mathrm{prueba}}}{I_{\mathrm{prueba}}}

RTh is the resistance seen at the terminals with independent sources killed.

Linear resistive DC network; unloaded divider unless RL is stated.

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Norton current

viz

I_N=I_{\mathrm{sc}}

IN is the short-circuit current of the Norton equivalent.

Linear resistive DC network; unloaded divider unless RL is stated.

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Norton resistance

viz

R_N=R_{\mathrm{Th}}

RN equals RTh: the same resistance in the Norton equivalent.

Linear resistive DC network; unloaded divider unless RL is stated.

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Thévenin–Norton equivalence

viz

V_{\mathrm{Th}}=I_NR_N

The equivalents satisfy VTh = IN RN and swap without changing Vo on RL.

Linear resistive DC network; unloaded divider unless RL is stated.

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Maximum power transfer

R_L=R_{\mathrm{Th}},\qquad P_{\max}=\frac{V_{\mathrm{Th}}^2}{4R_{\mathrm{Th}}}

Computes Maximum power transfer from the circuit model and the stated conditions.

Linear resistive DC network; unloaded divider unless RL is stated.

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Superposition principle

x=\sum_k x_k

Computes Superposition principle from the circuit model and the stated conditions.

Linear resistive DC network; unloaded divider unless RL is stated.

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Nodal analysis with KCL

\sum_k\frac{V_n-V_k}{R_{nk}}=I_n

Computes Nodal analysis with KCL from the circuit model and the stated conditions.

Linear resistive DC network; unloaded divider unless RL is stated.

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Mesh analysis with KVL

\mathbf{R}\mathbf{I}=\mathbf{V}

Computes Mesh analysis with KVL from the circuit model and the stated conditions.

Linear resistive DC network; unloaded divider unless RL is stated.

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