Linear Circuit Analysis
1. Introduction
2. Basic Concepts
- Charge, current, and voltage
- Power and energy
- Linear circuits
- Linear components
- Loops and nodes
- Series and parallel
- R, L & C combinations
- V & I combinations
3. Simple Circuits
- Ohm's law
- Kirchhoff's current law
- Kirchhoff's voltage law
- Single loop circuits
- Single node-pair circuits
- Voltage division
- Current division
4. Nodal and Mesh Analysis
5. Additional Analysis Techniques
- Superposition
- Source transformation
- The $V_{test}/I_{test}$ method
- Norton equivalent
- Thévenin equivalent
- Max power transfer
6. AC Analysis
7. Magnetically Coupled Circuits
8. Polyphase Systems
9. Operational Amplifiers
10. Laplace Transforms
11. Time-Dependent Circuits
- Introduction
- Inductors and capacitors
- First-order transients
- Nodal analysis
- Mesh analysis
- Laplace transforms
- Additional techniques
12. Two-Port Networks
Appendix
How to Type Equations
CircuitsU has two equations editors that you can use to write and submit formulas or equations:
- The 2-D Equation Editor (default)
- The 1-D Equation Editor
2-D Equation Editor
The 2-D Equation Editor allows you to type equations in a nice (printable) format. The editor is relatively easy to use and you can introduce subscripts, superscipts (i.e. powers), fractions, integrals and derivatives. You can activate the virtual keyboard to see the list of recommended symbols and variables.
Here are a few examples that you can try:
1-D Equation Editor
The 1-D Equation Editor allows you to type equations as a one-dimensional string. The tables below shows what you need to type to submit various formulas or equations. If you want to submit multiple equations in the same textbox you needs to write each equation on a separate line. To submit a single line answer (such as the final answer in a problem) you can type the final numerical value with or without any units or the analytical formula. Notice that
To submit... | type... |
---|---|
$1.234\times10^{-3}$ | 0.001234 1.234e-3 1.234m (use postfixes for powers of 10: n for $10^{-9}$, u for $10^{-6}$, m for $10^{-3}$, k for $10^3$, M for $10^6$, and G for $10^9$) |
$I_0=2\:{\textcolor{gray}A}$ | I0=2 A I0=2 (units are optional)2 A (you don't need to specify the sought variable if you submit a single-line answer)2 |
$V_0=2\:{\textcolor{gray}{kV}}$ | V0=2000 V V0=2000 (units are optional)2000 2e3 2k |
$45°$ | 45 deg 45deg 45° |
$45 \: \textcolor{gray}{rad}$ | 45 rad 45rad |
To submit... | type... |
---|---|
$R_1+R_2+R_3$ | R1+R2+R2 |
$\frac{R_1 R_2}{R_1+R_2}$ | R1*R2/(R1+R2) (the multiplication sign between R1 and R2 is mandatory in this case) |
$\frac{1}{\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}}$ | 1/(1/C1+1/C2+1/C3) or (1/C1+1/C2+1/C3)^(-1) |
$\frac{1}{\textcolor{blue}{j}\omega C}+j\omega L$ | 1/(jwC)+jwL |
$P_d= R_1 (i_2-i_3)^2$ | Pd=R1*(i2-i3)^2 Pd=R1(i2-i3)^2 (the multiplication sign is optional when multiplying a number with a symbolic quantity)R1(i2-i3)^2 (it is optional to specify the sought variable if you submit a single-line answer) |
$2\times 10^6\times [3-(a+b)]$ | 2M*(3-(a+b)) (replace square brackets with paranthesis)2M(3-(a+b)) |
$2 i_1+ R_1 I_x -7 = 0$ | 2*i1+R1/Ix-7=0 (if you submit an equation make sure you don't forget the equal sign)2i1+R1/Ix-7=0 |
$i_1=\frac{v_1-v_2}{R1}-\frac{v_3}{6.5}$ | (v1-v2)/R1-v3/6.5=0 |
$\frac{i_1}{2 \textcolor{blue}{j}}+3j(i_1-i_2)$ | 0=i1/(2*j)+3*j*(i1-i2) ($\textcolor{blue}{j}$ denotes imaginary number $\textcolor{blue}{j}=\sqrt{-1}$)0=i1/(2j)+3j(i1-i2) |
To submit... | type... |
---|---|
$\dfrac{dv_{1}(t)}{dt}$ | derivative(v1(t),t) |
$\dfrac{dv_{1}}{dt}$ (incorrect) | It is incorrect to use derivative(v1,t) (see the above line for the correct expression). You need to show the time dependance explicitly when referring to time-dependent quantities in CircuitsU. Therefore, you need v1(t) instead of v1 . |
$\int_{0}^{t}i_{1}(t){dt}$ | integral(i1(t),t) |
$\int_{0}^{t}i_{1}{dt}$ (incorrect) | It is incorrect to use integral(v1,t) (see the above line for the correct expression). You need to show the time dependance explicitly when referring to time-dependent quantities in CircuitsU. Therefore, you need i1(t) instead of i1 . |
$I(t)=C\dfrac{d[v_{1}(t)-v_{2}(t)]}{dt}$ | I(t)=C*derivative(v1(t)-v2(t),t) |
$I(t)=\frac{1}{L}\int_{0}^{t}[v_{1}(t)-v_{2}(t)]{dt}$ | I(t)=1/L*integral(v1(t)-v2(t),t) |
Note that the constants and functions shown in see Table 4 might not always be available when you submit answers. Their availability depends on what you are asked to submit at that particular step.
Constant/Function | Code |
---|---|
$\textcolor{blue}{j}=\sqrt{-1}$ | j |
$\omega$ | omega or w |
$\pi$ | pi or 3.14 |
$e^x$ | exp(x) e^x |
$a^b$ | a^b |
$\sqrt{x}$ | sqrt(x) x^0.5 |
$\sin(x)$ | sin(x) |
$\cos(x)$ | cos(x) E.g.: cos(45 deg) or cos(0.785 rad) |