AlexDev404/consolidated_formulas.md

## consolidated_formulas.md

      
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              consolidated_formulas.md
            
          
    Chapter 2: Voltage, Current, and Resistance


Concept
Formula
Citation


Voltage (V)
$V = \frac{W}{Q}$
[1-3]


Current (I)
$I = \frac{Q}{t}$
[4]


Conductance (G)
$G = \frac{1}{R}$
[5]


Wire Resistance (R)
$R = \rho \frac{l}{A}$
[6]


Chapter 3: Ohm’s Law, Energy, and Power


Concept
Formula
Citation


Ohm’s Law (Current)
$I = \frac{V}{R}$
[7]


Ohm’s Law (Voltage)
$V = IR$
[7]


Ohm’s Law (Resistance)
$R = \frac{V}{I}$
[8]


Power (Definition)
$P = \frac{W}{t}$
[9]


Watt’s Law (V and I)
$P = VI$
[10, 11]


Watt’s Law (I and R)
$P = I^2 R$
[10]


Watt’s Law (V and R)
$P = \frac{V^2}{R}$
[10, 11]


Chapter 4: Series Circuits


Concept
Formula
Citation


Kirchhoff’s Voltage Law (KVL)
$\sum_{i=1}^{n} V_i = 0$
[12]


Voltage Divider Rule (for $V_2$)
$V_2 = V_S \left(\frac{R_2}{R_T}\right)$
[13]


Chapter 5: Parallel Circuits


Concept
Formula
Citation


Total Parallel Resistance (General)
$\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \dots + \frac{1}{R_n}$
[14]


Total Parallel Resistance (Product-Over-Sum, 2 R)
$R_T = \frac{R_1 R_2}{R_1 + R_2}$
[15]


Current Divider (for $I_1$ in 2 resistors)
$I_1 = I_T \left(\frac{R_2}{R_1 + R_2}\right)$
[16]


Current Divider (for $I_2$ in 2 resistors)
$I_2 = I_T \left(\frac{R_1}{R_1 + R_2}\right)$
[16]


Chapter 6: Series-Parallel Circuits


Concept
Formula
Citation


Thevenin Voltage (using V-Divider)
$V_{TH} = V_S \left(\frac{R_2}{R_1 + R_2}\right)$
[17]


Load Voltage (using Thevenin)
$V_L = V_{TH} \left(\frac{R_L}{R_{TH} + R_L}\right)$
[18]


Chapter 8: Introduction to Alternating Current and Voltage


Concept
Formula
Citation


Period/Frequency Relationship

$T = \frac{1}{f}$ and $f = \frac{1}{T}$

[19]


Degrees to Radians
$\text{rad} = \text{degrees} \times \frac{\pi}{180}$
[20]


Radians to Degrees
$\text{degrees} = \text{rad} \times \frac{180}{\pi}$
[20]


Instantaneous Voltage (No phase shift)
$v = V_p \sin \theta$
[21]


Instantaneous Voltage (With phase shift)
$v = V_p \sin (\theta \pm \phi)$
[22]


Peak-to-Peak Voltage
$V_{pp} = 2 \times V_p$
[23]


RMS Voltage
$V_{rms} = 0.707 \times V_p$
[23, 24]


Average Voltage (Half-wave)
$V_{avg} = 0.637 \times V_p$
[25]


AC Power (Watt's Law - V and I)
$P = V_{rms} I_{rms}$
[26]


AC Power (Watt's Law - V and R)
$P = \frac{V_{rms}^2}{R}$
[26]


AC Power (Watt's Law - I and R)
$P = I_{rms}^2 R$
[26]


Chapter 9: Capacitors


Concept
Formula
Citation


Capacitance (C)
$C = \frac{Q}{V}$
[27]


Charge Stored (Q)
$Q = CV$
[27, 28]


Energy Stored (W)
$W = \frac{1}{2} C V^2$
[28]


Capacitance (Physical)
$C = \epsilon_r \left(8.85 \times 10^{-12} \text{ F/m}\right) \left(\frac{A}{d}\right)$
[29, 30]


Series Capacitance (Reciprocal Sum)
$\frac{1}{C_T} = \frac{1}{C_1} + \frac{1}{C_2} + \dots + \frac{1}{C_n}$
[31]


Series Capacitance (Product-Over-Sum, 2 C)
$C_T = \frac{C_1 C_2}{C_1 + C_2}$
[31]


Parallel Capacitance (Sum)
$C_T = C_1 + C_2 + C_3 + \dots + C_n$
[32]


Capacitive Reactance ($X_C$)
$X_C = \frac{1}{2\pi fC}$
[33]


Total Series Reactance
$X_{C_{tot}} = X_{C1} + X_{C2} + X_{C3} + \dots + X_{C_n}$
[33]


Total Parallel Reactance (Reciprocal Sum)
$\frac{1}{X_{C_{tot}}} = \frac{1}{X_{C1}} + \frac{1}{X_{C2}} + \dots + \frac{1}{X_{C_n}}$
[34]


Capacitive Voltage Divider ($V_{out}$ using $X_C$)
$V_{out} = V_S \left(\frac{X_{C2}}{X_{C_{tot}}}\right)$
[35]


Capacitive Voltage Divider ($V_{out}$ using $C$)
$V_{out} = V_S \left(\frac{C_{tot}}{C_2}\right)$
[36]


## unlabeled_consolidated.md

      
    Raw
  

              unlabeled_consolidated.md
            
          
Concept
Formula
Citation


Voltage (V)
$V = \frac{W}{Q}$
[1-3]


Current (I)
$I = \frac{Q}{t}$
[4]


Conductance (G)
$G = \frac{1}{R}$
[5]


Wire Resistance (R)
$R = \rho \frac{l}{A}$
[6]


Concept
Formula
Citation


Ohm’s Law (Current)
$I = \frac{V}{R}$
[7]


Ohm’s Law (Voltage)
$V = IR$
[7]


Ohm’s Law (Resistance)
$R = \frac{V}{I}$
[8]


Power (Definition)
$P = \frac{W}{t}$
[9]


Watt’s Law (V and I)
$P = VI$
[10, 11]


Watt’s Law (I and R)
$P = I^2 R$
[10]


Watt’s Law (V and R)
$P = \frac{V^2}{R}$
[10, 11]


Concept
Formula
Citation


Kirchhoff’s Voltage Law (KVL)
$\sum_{i=1}^{n} V_i = 0$
[12]


Voltage Divider Rule (for $V_2$)
$V_2 = V_S \left(\frac{R_2}{R_T}\right)$
[13]


Concept
Formula
Citation


Total Parallel Resistance (General)
$\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \dots + \frac{1}{R_n}$
[14]


Total Parallel Resistance (Product-Over-Sum, 2 R)
$R_T = \frac{R_1 R_2}{R_1 + R_2}$
[15]


Current Divider (for $I_1$ in 2 resistors)
$I_1 = I_T \left(\frac{R_2}{R_1 + R_2}\right)$
[16]


Current Divider (for $I_2$ in 2 resistors)
$I_2 = I_T \left(\frac{R_1}{R_1 + R_2}\right)$
[16]


Concept
Formula
Citation


Thevenin Voltage (using V-Divider)
$V_{TH} = V_S \left(\frac{R_2}{R_1 + R_2}\right)$
[17]


Load Voltage (using Thevenin)
$V_L = V_{TH} \left(\frac{R_L}{R_{TH} + R_L}\right)$
[18]


Concept
Formula
Citation


Period/Frequency Relationship

$T = \frac{1}{f}$ and $f = \frac{1}{T}$

[19]


Degrees to Radians
$\text{rad} = \text{degrees} \times \frac{\pi}{180}$
[20]


Radians to Degrees
$\text{degrees} = \text{rad} \times \frac{180}{\pi}$
[20]


Instantaneous Voltage (No phase shift)
$v = V_p \sin \theta$
[21]


Instantaneous Voltage (With phase shift)
$v = V_p \sin (\theta \pm \phi)$
[22]


Peak-to-Peak Voltage
$V_{pp} = 2 \times V_p$
[23]


RMS Voltage
$V_{rms} = 0.707 \times V_p$
[23, 24]


Average Voltage (Half-wave)
$V_{avg} = 0.637 \times V_p$
[25]


AC Power (Watt's Law - V and I)
$P = V_{rms} I_{rms}$
[26]


AC Power (Watt's Law - V and R)
$P = \frac{V_{rms}^2}{R}$
[26]


AC Power (Watt's Law - I and R)
$P = I_{rms}^2 R$
[26]


Concept
Formula
Citation


Capacitance (C)
$C = \frac{Q}{V}$
[27]


Charge Stored (Q)
$Q = CV$
[27, 28]


Energy Stored (W)
$W = \frac{1}{2} C V^2$
[28]


Capacitance (Physical)
$C = \epsilon_r \left(8.85 \times 10^{-12} \text{ F/m}\right) \left(\frac{A}{d}\right)$
[29, 30]


Series Capacitance (Reciprocal Sum)
$\frac{1}{C_T} = \frac{1}{C_1} + \frac{1}{C_2} + \dots + \frac{1}{C_n}$
[31]


Series Capacitance (Product-Over-Sum, 2 C)
$C_T = \frac{C_1 C_2}{C_1 + C_2}$
[31]


Parallel Capacitance (Sum)
$C_T = C_1 + C_2 + C_3 + \dots + C_n$
[32]


Capacitive Reactance ($X_C$)
$X_C = \frac{1}{2\pi fC}$
[33]


Total Series Reactance
$X_{C_{tot}} = X_{C1} + X_{C2} + X_{C3} + \dots + X_{C_n}$
[33]


Total Parallel Reactance (Reciprocal Sum)
$\frac{1}{X_{C_{tot}}} = \frac{1}{X_{C1}} + \frac{1}{X_{C2}} + \dots + \frac{1}{X_{C_n}}$
[34]


Capacitive Voltage Divider ($V_{out}$ using $X_C$)
$V_{out} = V_S \left(\frac{X_{C2}}{X_{C_{tot}}}\right)$
[35]


Capacitive Voltage Divider ($V_{out}$ using $C$)
$V_{out} = V_S \left(\frac{C_{tot}}{C_2}\right)$
[36]
Concept	Formula	Citation
Voltage (V)	$V = \frac{W}{Q}$	[1-3]
Current (I)	$I = \frac{Q}{t}$	[4]
Conductance (G)	$G = \frac{1}{R}$	[5]
Wire Resistance (R)	$R = \rho \frac{l}{A}$	[6]
Concept	Formula	Citation
Ohm’s Law (Current)	$I = \frac{V}{R}$	[7]
Ohm’s Law (Voltage)	$V = IR$	[7]
Ohm’s Law (Resistance)	$R = \frac{V}{I}$	[8]
Power (Definition)	$P = \frac{W}{t}$	[9]
Watt’s Law (V and I)	$P = VI$	[10, 11]
Watt’s Law (I and R)	$P = I^2 R$	[10]
Watt’s Law (V and R)	$P = \frac{V^2}{R}$	[10, 11]
Concept	Formula	Citation
Kirchhoff’s Voltage Law (KVL)	$\sum_{i=1}^{n} V_i = 0$	[12]
Voltage Divider Rule (for $V_2$)	$V_2 = V_S \left(\frac{R_2}{R_T}\right)$	[13]
Concept	Formula	Citation
Total Parallel Resistance (General)	$\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \dots + \frac{1}{R_n}$	[14]
Total Parallel Resistance (Product-Over-Sum, 2 R)	$R_T = \frac{R_1 R_2}{R_1 + R_2}$	[15]
Current Divider (for $I_1$ in 2 resistors)	$I_1 = I_T \left(\frac{R_2}{R_1 + R_2}\right)$	[16]
Current Divider (for $I_2$ in 2 resistors)	$I_2 = I_T \left(\frac{R_1}{R_1 + R_2}\right)$	[16]
Concept	Formula	Citation
Thevenin Voltage (using V-Divider)	$V_{TH} = V_S \left(\frac{R_2}{R_1 + R_2}\right)$	[17]
Load Voltage (using Thevenin)	$V_L = V_{TH} \left(\frac{R_L}{R_{TH} + R_L}\right)$	[18]
Concept	Formula	Citation
Period/Frequency Relationship	$T = \frac{1}{f}$ and $f = \frac{1}{T}$	[19]
Degrees to Radians	$\text{rad} = \text{degrees} \times \frac{\pi}{180}$	[20]
Radians to Degrees	$\text{degrees} = \text{rad} \times \frac{180}{\pi}$	[20]
Instantaneous Voltage (No phase shift)	$v = V_p \sin \theta$	[21]
Instantaneous Voltage (With phase shift)	$v = V_p \sin (\theta \pm \phi)$	[22]
Peak-to-Peak Voltage	$V_{pp} = 2 \times V_p$	[23]
RMS Voltage	$V_{rms} = 0.707 \times V_p$	[23, 24]
Average Voltage (Half-wave)	$V_{avg} = 0.637 \times V_p$	[25]
AC Power (Watt's Law - V and I)	$P = V_{rms} I_{rms}$	[26]
AC Power (Watt's Law - V and R)	$P = \frac{V_{rms}^2}{R}$	[26]
AC Power (Watt's Law - I and R)	$P = I_{rms}^2 R$	[26]
Concept	Formula	Citation
Capacitance (C)	$C = \frac{Q}{V}$	[27]
Charge Stored (Q)	$Q = CV$	[27, 28]
Energy Stored (W)	$W = \frac{1}{2} C V^2$	[28]
Capacitance (Physical)	$C = \epsilon_r \left(8.85 \times 10^{-12} \text{ F/m}\right) \left(\frac{A}{d}\right)$	[29, 30]
Series Capacitance (Reciprocal Sum)	$\frac{1}{C_T} = \frac{1}{C_1} + \frac{1}{C_2} + \dots + \frac{1}{C_n}$	[31]
Series Capacitance (Product-Over-Sum, 2 C)	$C_T = \frac{C_1 C_2}{C_1 + C_2}$	[31]
Parallel Capacitance (Sum)	$C_T = C_1 + C_2 + C_3 + \dots + C_n$	[32]
Capacitive Reactance ($X_C$)	$X_C = \frac{1}{2\pi fC}$	[33]
Total Series Reactance	$X_{C_{tot}} = X_{C1} + X_{C2} + X_{C3} + \dots + X_{C_n}$	[33]
Total Parallel Reactance (Reciprocal Sum)	$\frac{1}{X_{C_{tot}}} = \frac{1}{X_{C1}} + \frac{1}{X_{C2}} + \dots + \frac{1}{X_{C_n}}$	[34]
Capacitive Voltage Divider ($V_{out}$ using $X_C$)	$V_{out} = V_S \left(\frac{X_{C2}}{X_{C_{tot}}}\right)$	[35]
Capacitive Voltage Divider ($V_{out}$ using $C$)	$V_{out} = V_S \left(\frac{C_{tot}}{C_2}\right)$	[36]