Circuits midterm 1

equations, concepts, and step by step

KVL Big rule

V_Loop = 0V

Conservation of energy

must stay consistent

KVL and KCL voltage and current direction

entering node = +, leaving node= —

Passive convention

if voltage direction is forced , current direction is forced, vice versa

Electrical Resistance - Ohms law on graph

V= IR

V = y axis

I = x axis

R = slope

KCL Big rule

I_loop = 0A

Conservation of charge

must stay consistent

Circuit Analysis

1. Assign refernce direction

2. Basic circuit element: Nodes & loops, K laws

3. check anwer with Power balance

Power balance

total power absorbed + total power delivered = 0

Passive sign convention for power

Power > 0W = absorbed

Power < 0W = Delivered

Ohms law on graph = R linear

P_v = (+)(+)

P_v = (-)(-)

Independent Voltage

Independent Current Source

Open circuit for ohms law

current = 0 A

Resistance = infinte

Voltage still present

Open circuit

An open circuit means the electrical loop is incomplete, so no electricity moves through the device.

Short circuit in terms of ohms law

current = infinte

Resistance = 0

Voltage still present

Short circuit

A short circuit happens when electricity skips the intended load (like a light or motor) and takes a shortcut with almost zero resistance.

Voltage and Current divider

a quick way to determine the wanted current or voltage with ohms law, resistance equivalence, and the equation

V_{want =} V_total (R_want / R_EQ)

Current Division Rule

• The current division rule applies to parallel circuits where a total current splits among different branches.

• Notice that the numerator uses the opposite branch's resistance

Voltage Division Rule

The voltage division rule applies to series circuits where a total supply voltage shares across components

• use the same resistance whose voltage you want to find

Dependent Source

Voltage of a current source that is dependent upon a different voltage or current.

Independent Voltage Source

True

Voltage controlling source

True

Voltage dependent source

True

Combined Constraints

1. Identify elements: voltage and current, passive sign convention

2. Identify nodes and loops, and write KVL and KCL equations

3. Solve the system of equations

Element constraints

• voltage and current elements, passive sign constraints

Connection Constraints

Identify nodes and loops, and write KVL and KCL equations

Combined Constraints

Solving the KCL and KVL system of equations

Element Equation

Total elements in circuit: voltage and current source, and resistors

KCL equation

total Nodes -1

KVL equations

Elements - N + 1

Total independent equations

Element Equations + KCL equations + KVL equations

Node Voltage analysis

only works with essential node, reference node, ground

essential node

a connection point in an electrical circuit where three or more circuit elements or branches meet

reference node

a single point in an electrical circuit assigned a potential of zero volts (0 V) to serve as a common baseline for measuring all other node voltages. The V_c if you will.

Ground

It gives electric current a safe path to return to its source and complete the circuit.

Steps for Node Voltage Analysis

1. Select reference node

2. Highlight & Label Nodes

3. KCL @ N - M - 1

   1. I_R = (V_tail - V_{arrow )/ R}

4. Solve system of equations

5. Back-solve to find currents

modified KCL equation

Supernode

Voltage source is not referenced to ground, not directly connected to ground

Writing equations for Supernode

treat nodes connected to floating voltage source as single node. Equations modeled like modified node anaylsis KCL equation

Source transformantion

Convert b/w independent voltage & current sources @ interface. done with ohms law

• related to thevenin & norton equivalent circuits

Thevenin & Norton Equivalent Circuits

Modeling used to design interfaces → complex circuits in a simple circuit with only a single independent source, equivalent resistance, and resistor load

Thevenin Equivalent equation

V_TH = I_L * R_TH

Norton resistance

same as thevenin resistance

External Test Source Method Equivalent Resistance

• used when there is dependent source in circuit

• 1. turn of independent source

• 2. replace load with an external test source

  • Independent voltage or current, Label V_T / I_T

• Solve for V_T / I_T = R_TH

Norton Equivalent Current

Current as seen by the load → need to short circuit

Thevenin Equivalent Voltage

• V_TH

• _{Voltage source as seen by the load → Need Open-CIrcuit}

Norton equation

V_{TH =} I_{N *} R_TH

Maximum Power Transfer

For a fixed source & variable load, it is the maximum possible power delivered to the load

Maximum Power Transfer equation

When does Max Power occur

Matched load.

when R_load = R_TH

Superposition Principle

For Linear System where Total response of a system is the

sum of the individual responses

How to Apply Superposition?

1. Turn off the opposite independent source

2. Analyze the circuit with the desired method.

3. When all parameters are found, sum them for the total.