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## Class 12 Physics (India)

### Unit 3: Lesson 7

Kirchhoff's junction rule

# Circuit terminology

Glossary of terms we need to talk about circuits and schematics. Nodes, branches, loops and meshes, reference node and ground, and schematic "equivalence." Written by Willy McAllister.
We are developing methods for analyzing a circuit. So far we've defined the most common components (resistor, capacitor, and inductor) and sources (voltage and current). Now we need a crisp vocabulary to talk about circuits. This article is a glossary of terms and concepts we use in circuit analysis and design.

## Circuit

Circuit comes from the word circle. A circuit is a collection of real components, power sources, and signal sources, all connected so current can flow in a complete circle.
Closed circuit – A circuit is closed if the circle is complete, if all currents have a path back to where they came from.
Open circuit – A circuit is open if the circle is not complete, if there is a gap or opening in the path.
Short circuit – A short happens when a path of low resistance is connected (usually by mistake) to a component. The resistor shown below is the intended path for current, and the curved wire going around it is the short. Current is diverted away from its intended path, sometimes with damaging results. The wire shorts out the resistor by providing a low-resistance path for current (probably not what the designer intended).
Make or Break – You make a circuit by closing the current path, such as when you close a switch. Breaking a circuit is the opposite. Opening a switch breaks the circuit.

## Schematic

A schematic is a drawing of a circuit. A schematic represents circuit elements with symbols and connections as lines.
Elements – The term elements means "components and sources."
Symbols – Elements are represented in schematics by symbols. Symbols for common 2-terminal elements are shown here,
Lines – Connections between elements are drawn as lines, which we often think of as "wires". On a schematic, these lines represent perfect conductors with zero resistance. Every component or source terminal touched by a line is at the same voltage.
Dots – Connections between lines can be indicated by dots. Dots are an unambiguous indication that lines are connected. If the connection is obvious, you don't have to use a dot.
(a) and (b) are both good
(c) no dot indicates no connection
(d) also indicates no connection; the horizontal wire "hops" over the vertical wire. (d) is very clear but takes extra effort and space to draw.
(e) for crossing connected lines, (e) is acceptable, but risks looking too much like (c), so (f) is the better practice.
Reference designator – When you place a component in a schematic you often give it a unique name, known as a reference designator. Examples of reference designators are start text, R, 1, end text, start text, C, 6, end text, and start text, V, end text, start subscript, start text, B, A, T, end text, end subscript. The 1 in start text, R, 1, end text is part of the name, and does not indicate the resistance value. Reference designators are by definition unique for each schematic. They let you identify components by name even if some of them have the same value. It is okay to use reference designators in equations. start text, R, 1, end text can be assigned a resistance value, start text, R, 1, end text, equals, 4, point, 7, start text, k, end text, \Omega, and it can be used as a variable in expressions, as in start text, R, 2, end text, dot, start text, C, 6, end text, equals, 4, point, 7, start text, k, end text, \Omega, dot, 2, mu, start text, F, end text.
Reference designators give components unique names, even if their values are the same.
Node – A junction where 2 or more elements connect is called a node. The schematic below shows a single node (the black dot) formed by the junction of five elements (abstractly represented by orange rectangles).
Since lines on a schematic represent perfect zero-resistance conductors, there is no rule that says lines from multiple elements are required to meet in a single point junction. We can draw the same node as a distributed node like the one in the schematic below. These two representations of the node mean exactly the same thing.
A distributed node might be all spread out, with lots of line segments, elbows, and dots. Don't be distracted, it is all just one single node. Connecting schematic elements with perfect conductors means the voltage everywhere on a distributed node is the same.
Here is a realistic-looking schematic with the distributed nodes labeled:
problem 1
How many nodes are in this schematic?

BranchBranches are the connections between nodes. A branch is an element (resistor, capacitor, source, etc.). The number of branches in a circuit is equal to the number of elements.
problem 2
How many branches are in this schematic?

Loop – A loop is any closed path going through circuit elements. To draw a loop, select any node as a starting point and draw a path through elements and nodes until the path comes back to the node where you started. There is only one rule: a loop can visit (pass through) a node only one time. It is ok if loops overlap or contain other loops. Some of the loops in our circuit are shown here. (You can find others, too. If I counted right, there are six.)
Mesh – A mesh is a loop that has no other loops inside it. You can think of this as one mesh for each "open window" of a circuit.
problem 3
How many meshes are in this circuit?

Reference Node – During circuit analysis we usually pick one of the nodes in the circuit to be the reference node. Voltages at other nodes are measured relative to the reference node. Any node can be the reference, but two common choices that simplify circuit analysis are,
• the negative terminal of the voltage or current source powering the circuit, or
• the node connected to the greatest number of branches.
Ground – The reference node is often referred to as ground. The concept of ground has three important meanings.
A metal stake driven into the ground next to a home. The wire clamped to the stake curves up to the right to provide the safety ground reference for the home's electrical system. Sometimes the grounding wire is clamped to a water pipe where the pipe disappears into the Earth.
Ground is
• the reference point from which voltages are measured.
• the return path for electric current back to its source.
• a direct physical connection to the Earth, which is important for safety.
The ground node gets its name from the third meaning. But the other two are equally important.
You will come across various symbols for ground:

## Schematic equivalence

We need to take a second to talk about the idea of schematic equivalence. This is important because a circuit can be represented by schematics drawn in different ways.
The following two schematics are drawn differently. The schematic on the left shows a voltage source and three resistors in numerical order. In the schematic the right, resistor start text, R, end text, 3 appears to the left of the voltage source.
Do both of these schematics properly represent the intended circuit? Or said another way,
Are these two schematics equivalent?
We say a real circuit and a schematic (or two schematics), are equivalent if they have the same nodes and branches.
To be equivalent, two schematics must:
• Represent every component and source
• Have the same number of nodes
• Each node must be connected to the same branches
Let's check to see if our two schematics are equivalent:
• Are all components and sources represented in both schematics?
Roll call ... start text, V, end text, here!, start text, R, end text, 1, here!, start text, R, end text, 2, here! start text, R, end text, 3, here!
All elements accounted for.
• Do both schematics have the same number of nodes?
Yes. Both schematics have 2 nodes.
• Is each node connected to the same branches?
– Yes. Each node connects to the three resistors and a source.
The two nodes are marked with orange lines. The four branches are shown as blue arrows.
So the answer is: yes, these schematics are equivalent.
Equivalence means the matching nodes will have the same voltage, and the matching branches will have the same current. These are the things we care about being the same.
You could build a real circuit based on either of these schematics. Lay the physical wires and components right on top of either drawing and solder them together. Both schematics will produce the intended circuit, with identical node voltages and branch currents.
This discussion of equivalence may seem rather overdone; what's the big deal? Schematics have a curious property that often catches beginners.

## A schematic puzzle

I'm going to point out something that may seem baffling, (but only for a moment). As we just established, the following two schematics are equivalent. But, not everything is exactly the same. The individual point-to-point connections of the lines between elements are not the same.
Look at the blue arrow in the left schematic. That wire carries the current flowing towards start text, R, end text, 2 and start text, R, end text, 3.
Can you find the equivalent wire in the schematic on the right?
(Find a wire carrying the current going to start text, R, end text, 2 and start text, R, end text, 3.)
What is going on? It is a trick question, to highlight something about the nature of schematics.
This puzzle reveals a fundamental difference between a real circuit and a drawn schematic. The lines in a schematic diagram do not necessarily represent the specific point-to-point order of the connections the corresponding real circuit might have. The question about one wire carrying current to start text, R, end text, 2 and start text, R, end text, 3 assumes a specific wiring order that does not exist in the schematic on the right.
How do you avoid getting trapped by this schematic puzzle? You can always count on identical branch currents in every equivalent schematic or real circuit. So always think about current flowing in a branch (flowing in a component or source), not current flowing in a "wire." Currents in "wires" may or may not exist in an equivalent version of the schematic, or in the real circuit built from either schematic.

### Concept check: Equivalence

Which of these schematics represent the same circuit (are equivalent)?
Assume all resistors have the same value.
Take your time, this isn't simple.

## Drawing a good schematic

A good schematic serves a number of noble purposes. A good schematic
• captures the design of a circuit in an unambiguous way.
• allows you to share your design with other people.
• helps you remember how your circuit works, even a month from now.
Both you and your colleagues will appreciate these drawing habits for creating good schematics,
• Place inputs on the left, and outputs on the right.
• Let information flow from left to right across the circuit.
• Use up/down on the page to suggest voltage levels. That is, draw higher voltage wires closer to the top of the page, and lower voltages (like ground) near the bottom of the page.
The following schematics are equivalent, but the one on the left is not as easy to read as the one on the right. The one on the right follows the guidelines for a good schematic.
Good schematics capture your design intent. You convey your meaning more quickly and reliably if you draw schematics to make it obvious what you are trying to do.
As you are asked to read different schematics, take a moment to notice the drawing style. Mimic the drawing style of schematics you find easy to read. Put your creativity into the circuit design, not into drawing a schematic in a new style.
We now have a full vocabulary for talking about circuits and their sub-parts. We are ready to start analyzing.

## Want to join the conversation?

• this is a good start, but this electronics portion of Kahn Academy needs a lot of work. It has the potential to be great however, as it seems to be one of the only resources out there. Thanks
• What does the voltage of a node measured against ground do to the voltage across other circuit elements in a circuit? If the voltage of a node measured against ground is 1 volt, will it increase the voltage across all circuit elements in a circuit by 1 volt?
• Yes, if the voltage supply in the circuit featured in "A schematic puzzle" is one volt, each resistor (R1, R2, R3) will have 1 volt across it with respect to ground. All of the resistors are connected to the same "place" on the voltage source, so they all have equal potential across them with respect to ground. Using Ohm's law (V=IR) you can then calculate the current through each resistor and solve the circuit.
• I'm a bit confused about the second answer the the equivalence concept check. C,F and H each have one node connected to 3 resistors and another connected to 1 source and one resistor. However the third node of C and F are connected to 2 resistors and the source, whereas the third node on H is connected to three resistors and the source. Maybe I've misunderstood :)
• Check circuit H one more time. The + terminal of the voltage source is connected to two resistors, just like C and F. When I trace out circuit puzzles like this, I like to pick one or two distinctive features of a specific element to start tracing from. In this case, the terminals of the voltage source. This works better for me than keying off a node, because the shape of a node is arbitrary and changes for each version of the schematic.
• What is the concept of ground ?
• The article states that ground is, "the reference point from which voltages are measured (1), the return path for electric current back to its source (2), or a direct physical connection to the Earth, which is important for safety. (3)"

(1) It's like a reference frame for one/two dimensional motion in physics. It also is 0 volts

(2) Usually in schematics, you can see the ground part of the circuit right before the source in the bottom left corner.
• I had trouble understanding what a short was when i read it until i sat for a minute. I want to know if my thought process is right before i continue. I know that it is when there is a lower resistance somewhere where it shouldn't be. That lower resistance raises the current (ohm's law) because the voltage is the same, which damages what the current was originally going through (in your example, the resistor). That's why water messes up electronics. It runs through the conductive particles in the water, lowering the resistance.
• You are very close. When you "short out" a resistor, you are adding a really small-valued resistor (like 0.001 ohms) right next to the original resistor. All the current that flowed in the original resistor now starts flowing through the "shorting wire". Ohm's Law says the current changes from i = v/R before the short to i = v/0.001 after the short. That tiny denominator makes i really big.

The thing you didn't quite get right is what gets damaged. The original resistor doesn't mind a bit. The big i current isn't flowing through the original resistor. The thing that suffers is the battery. It is being asked to provide a really big i, and it might not be able to.

The other thing that happens is that huge i generates a lot of heat. In a cell phone, the battery is connected to a special chip that regulates (keeps steady) the voltage for the rest of the phone. If you drop your phone in the "puddle," the water can short out either the battery or that special chip. In both cases the battery and the regulator chip fight like mad to keep the voltage where it is "supposed" to be, and they can die trying because of the internal heat they generate.
• How was that great circuit morphing animation done? I like it very much!
• I am a bit confused about short circuits, it says current is diverted away from its intended path, but then where does it go?
(1 vote)
• Consider an appliance such as vacuum cleaner plugged into an outlet at your house. Normally the current would flow out one terminal do some useful work in the appliance and return back on the other terminal. Let's call this the “normal” flow of say 10 A. In this article the appliance is the vertical resistor.

A short circuit is an “abnormal” flow of current. Lets assume the power cord leading to your appliance is damaged. Perhaps it was caught in a door or an animal gnawed away the insulation. The wire has been damaged and current flows somewhere it shouldn't. We now have a short circuit. The current is no longer 10 A but something much higher. To clarify, the appliance was the intended path, the crossed wires in the power cord is the short circuit.

These short circuits can be dangerous as the high current flow can cause heating – sometimes hot enough to start a fire. All homes should be equipped with a circuit breaker or fuse box to detect the short circuit and remove power from the faulty section.
• A battery (source of charge) has what two terminals?
(1 vote)
• One positive terminal, one negative terminal.