1) Ideal Independent Voltage Sources
An ideal independent voltage source is a two-terminal circuit element where the voltage across it
a) is independent of the current through it
b) can be specified independently of any other variable in a circuit.
There are two symbols for ideal independent voltage source in circuit theory:

The battery cell symbol is usually used for constant voltage sources but the other one is more general and can be used for both variable and constant voltage sources.
The v-i plot for an ideal independent voltage source is shown below.

In a circuit, voltage across elements which are parallel with voltage sources are equal to the voltage of the corresponding voltage sources. This is a useful rule in solving circuits. For example, check out the following problem.

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2) Ideal Independent Current Sources
In contrast to ideal independent voltage sources, an ideal independent current source is a two-terminal circuit element where the current passing through it
a) is independent of the voltage across it
b) can be specified independently of any other variable in a circuit.
There is one symbol for ideal independent current source in circuit theory:

The v-i plot for an ideal independent current source is depicted below.

Similar to voltage sources, the charactristic of ideal independent current sources can also be used to solve circuits (or a portion of a circuit) where an element is in series with a current source. Lets consider the following solved problem.

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1. 2. 3. 4. 5. 6. 1. khurram abbas says:

what is meant by loop analysis?

1. loop analysis (also known as mesh analysis) is an alternate to the nodal analysis. Both are used to solve circuits. In the loop analysis, the main unknowns are loop currents and other unknowns are written in terms of loop currents. KVL is used to obtain a set of equations where all unknowns are loop currents and by solving the set, loop currents can be found. A simple solved problem (one loop) is posted here. I am planning to post more and publish an e-book for mesh analysis as the one that I have published for the nodal analysis.

2. Gajendrasingh Rajput says:

What about dependent sources?

1. The value of a dependent sources is proportional to another voltage or current in the circuit. For example, if a dependent voltage source is \$latex 2V_{x}\$ this means that the voltage of that source is two times the voltage labeled as \$latex V_x\$ in the circuit. Solving circuits with dependent sources are usually trickier than the one without.

3. Gajendra Rajput says:

how to convert circuits contining idependent and dependent sources

1. We do not convert dependent sources to independent ones in analyzing circuits. Instead, we try to find the variable that the dependent source depends on, with respect to main unknowns and knowns, and use it in the analysis.

4. arnoldseeker says:

if a branch has only a voltage source connected to it then the resistance is not defined
how can i analyze this branch "nodaly"?!

1. If one of the voltgae source terminals is connected to the reference node, the voltage of the other node can be easily determined by the voltage source. Please download my e-book, this is thoroughly explained there. You may need to use supernode, if none of the terminals of the voltage source is the reference node.

5. arnoldseeker says:

sorry but why cant we use the superposition principal in the case of dependent sources analysis ?!

1. In superposition, you have to turn off all sources except one and find the summation of the contributions. If you keep a dependent source on and turn off all other sources, the output will be zero. Superposition is based on considering the circuit as a system with inputs and outputs. Inputs are independent sources and outputs are unknowns that we want to determine. Dependent sources are not inputs. They simply relates some voltages/currents to other voltages/currents. In other words, they are part of the system itself, similar to a resistor.

6. reddy says:

nice work .. its so clear and btw thanks

7. reddy says:

nice work........

8. abhilash sharma says:

how to treat the current sources while solving circuits also the voltage sources as well ?

9. what can you say about DC resistance of the diode over this linear portion?the linear portion is a silicon diode

1. Which portion?

10. anup says:

sir, what will be the time constant for series and parallel RLC ckt?

11. shaurya says:

what exactly are current sources?I was told that current sources are the one which supply current in a circuit and voltage sources are the one that supply potential difference across a circuit.What I am confused with is that the current sources should have a potential difference across them as no current can be drawn without pot difference,so a current source should also be a voltage source,then whats is the difference between current and voltage sources.
Thank You

1. The difference is that a voltage source keeps the voltage constant but a current source keeps the current constant. So, a voltage source does not care about the current, its duty is to keep the voltage as required. The current passing through a voltage source can be negative, zero or positive, it may vary by time but the voltage is constant for sure. A current source is the dual. Voltage across a current source can be positive, zero or negative or it can vary by time but the current is fixed. Do not try to find a simple physical element which matches with a current source. For a voltage source, a battery is a perfect match but there is no such a element which matches current sources that perfect. Some elements behave like current sources in some operating point.

12. sumi says:

Sir,
I have doubts regarding testing of power supplies with a constant voltage source (o- 30V)and constant current source (0 -25A). .When I connect a shunt of 50A and 75mv across a constant current source and vary from 1A to 20A I get the required mV across the shunt. What should the reading on the constant voltage source read?
Can you answer me on this email
sumi

13. vimala says:

can dependent and independent voltage sources be added to one

14. sir,current is nothing but flow of electrons.that is current is produced by voltage but voltage source and current source are used in a circuit at a time please explain.

1. Please refer to definition and do not mix up physical power sources with ideal independent sources which are models. You can model power sources with independent sources plus other elements depend on their operating point. As I said, for now think about ideal independent sources as models and do not take them equivalent to batteries or other physical sources.

An ideal independent voltage source is a two-terminal circuit element where the voltage across it
a) is independent of the current through it
b) can be specified independently of any other variable in a circuit.

15. current is produced by voltage .but why current source is indepedent of voltage as well as conversly

1. current passing through a 2V voltage source can be zero, 1A, 2A, 1000A, ... but its voltage is always 2V. So, voltage is independent from current.

16. dushyanth says:

Current source has infinity resistance right?
But in the problems above current seems to flow through it how is it possible?

1. That way of looking on sources could be misleading. Current source keeps current passing through constant equal to the source current value. Of course current passes through a current source.

17. zaid khan farar says:

sir whats about to solve the configuration if one resistor is series with other parallel resistor ......how can we solve it through current divider rule???