Dependent sources are circuit elements whose voltage or current is controlled by another voltage or current elsewhere in the circuit. In Electrical Circuits and Systems I, you use them to model devices like transistors and op-amps.
Dependent sources are circuit sources whose output is set by another circuit variable, called the controlling variable. That means the source is not fixed the way an independent voltage or current source is. Instead, its value changes according to a voltage or current elsewhere in the network.
In Electrical Circuits and Systems I, you usually see four forms: voltage-controlled voltage source, current-controlled voltage source, voltage-controlled current source, and current-controlled current source. The names tell you exactly what is being measured and what is being produced. For example, a voltage-controlled current source might output a current equal to a gain times some node voltage.
The big idea is that a dependent source lets you represent devices that amplify or respond to another signal. This is why they show up in simplified models of transistors, operational amplifiers, and other active circuits. You are not just solving for a source value by itself. You are tracing how one part of the circuit affects another part.
When you do nodal analysis, a dependent source does not get "turned off" or ignored. You keep it in the circuit and add an equation that links the source to its controlling variable. That extra equation is what makes the math work. If the controlling variable is a node voltage, you can often write it directly in terms of node unknowns. If it is a branch current, you may need an extra relationship from Ohm’s law or a labeled current expression.
A common mistake is treating a dependent source like a regular independent source during simplification. That breaks the circuit model because the source value is not fixed. Another trap is forgetting that the controlling variable may be somewhere else in the circuit, not right next to the source symbol. The arrow or polarity markings on the dependent source tell you both the output type and the reference direction, so read those carefully before you write equations.
Dependent sources show up whenever the course moves from simple resistor networks into circuits that actually behave like amplifiers or controlled systems. They are the bridge between "just solve for voltages and currents" and "model how one signal controls another." That matters in op-amp problems, transistor-style models, and any circuit where a small input affects a larger output.
They also make nodal analysis more realistic. A lot of textbook circuits are built around dependent sources because they force you to connect KCL equations with a control relation. If you can handle one, you can usually handle the extra equation structure in larger networks too.
They matter in superposition problems as well. Independent sources can be turned off one at a time, but dependent sources stay active because their value still depends on the rest of the circuit. That distinction shows up a lot on problem sets and quizzes, especially when you are asked to find a gain, a node voltage, or a branch current in a linear network.
If you can read a dependent source correctly, you can trace the signal path through the circuit instead of treating the diagram like a pile of symbols. That makes the rest of the chapter, especially nodal analysis and source-dependent models, much easier to work with.
Keep studying Electrical Circuits and Systems I Unit 4
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view galleryNodal Analysis
Dependent sources fit naturally into nodal analysis because you can write KCL at each node and then add the control equation that defines the source. If the dependent source is tied to a node voltage, it often becomes part of the same variable set you are already solving for. That makes it feel less like a special case and more like another equation in the system.
Superposition Principle
When you use superposition, dependent sources stay active because they are not independent excitations. Only independent voltage and current sources get turned off one at a time. This is a common place to lose points, since students sometimes erase every source in the circuit. The dependent source must remain so the circuit response stays correct.
Current Source
A dependent current source is one of the most common forms you will see. It may deliver a current based on a voltage elsewhere in the circuit or on another current in a different branch. That makes it useful for modeling gain and control behavior without needing a physical resistor-only description.
Controlling Variable
The controlling variable is the measured voltage or current that sets the dependent source output. You have to identify it before you can write the source equation. If the controlling variable is not labeled clearly, you may need to rewrite it using node voltages, branch currents, or Ohm's law so it matches the unknowns in your equations.
A quiz or problem-set question usually asks you to identify the controlling variable, write the dependent source equation, and solve the circuit with KCL or superposition. You might be given a circuit with a source like "5v_x" or "2i_x" and asked to find node voltages or branch currents.
The move is simple: do not delete the dependent source when simplifying the circuit. Instead, keep it in your equations and connect it to the variable it depends on. If the source is voltage-controlled, express that voltage in terms of node voltages. If it is current-controlled, express that current using a branch relation or another circuit equation.
You may also see a conceptual question asking why a source stays active in superposition, or a modeling question where you match a transistor-like circuit to a dependent-source form. The key is showing the relationship, not just naming the symbol.
An independent source has a fixed voltage or current that does not depend on anything else in the circuit. A dependent source changes with a controlling variable elsewhere in the network. In problem solving, that difference matters because independent sources can be turned off for superposition, while dependent sources cannot.
Dependent sources are sources whose voltage or current is set by another circuit variable, not by a fixed value.
The controlling variable can be a voltage or a current, and it may come from a different part of the circuit.
You keep dependent sources active in superposition because their value still depends on the remaining circuit variables.
In nodal analysis, a dependent source usually adds one more equation that links the source to the variable that controls it.
They are how simplified circuit models represent gain and control in devices like op-amps and transistors.
Dependent sources are circuit elements whose output voltage or current depends on another voltage or current in the same circuit. They are used to model controlled behavior, like amplification or signal-dependent output. In this course, you mostly see them in nodal analysis and source superposition problems.
An independent source keeps a fixed voltage or current no matter what the rest of the circuit does. A dependent source changes based on a controlling variable elsewhere in the circuit. That is why independent sources can be turned off in superposition, but dependent sources stay in the circuit.
You include it in the KCL equations like any other source, then add the equation that defines its controlling relationship. If the source depends on a node voltage, you can usually write that voltage directly from your node labels. If it depends on a current, you may need another expression from Ohm's law or a labeled branch current.
They stay on because they are not separate independent inputs. Their value still changes with the circuit variables that remain after you turn off the other independent sources. If you remove them, you change the circuit itself and get the wrong response.