Under what circumstances are two circuits considered equivalent? A. their input values are the same B. the output of one is the inverse of the output of the other C. their output values are the same for all possible input combinations D. their output values are always 1 E. the input of one matches the output of the other

B the output of one is the inverse of the output of the other

Explanation:

equivalent circuit refers to a theoretical circuit that retains all of the electrical characteristics of a given circuit. Often, an equivalent circuit is sought that simplifies calculation, and more broadly, that is a simplest form of a more complex circuit in order to aid analysis. In its most common form, an equivalent circuit is made up of linear, passive elements. However, more complex equivalent circuits are used that approximate the nonlinear behavior of the original circuit as well. These more complex circuits often are called macromodels of the original circuit. An example of a macromodel is the Boyle circuit for the 741 operational amplifier.

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Network Theory - Equivalent Circuits

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If a circuit consists of two or more similar passive elements and are connected in exclusively of series type or parallel type, then we can replace them with a single equivalent passive element. Hence, this circuit is called as an equivalent circuit.

In this chapter, let us discuss about the following two equivalent circuits.

Series Equivalent Circuit

Parallel Equivalent Circuit

Series Equivalent Circuit

If similar passive elements are connected in series, then the same current will flow through all these elements. But, the voltage gets divided across each element.

Consider the following circuit diagram.

Series Equivalent Circuit

It has a single voltage source (VS) and three resistors having resistances of R1, R2 and R3. All these elements are connected in series. The current IS flows through all these elements.

The above circuit has only one mesh. The KVL equation around this mesh is

VS=V1+V2+V3

Substitute V1=ISR1,V2=ISR2 and V3=ISR3 in the above equation.

VS=ISR1+ISR2+ISR3

⇒VS=IS(R1+R2+R3)

The above equation is in the form of VS=ISREq where,

REq=R1+R2+R3

The equivalent circuit diagram of the given circuit is shown in the following figure.

Equivalent Circuit

That means, if multiple resistors are connected in series, then we can replace them with an equivalent resistor. The resistance of this equivalent resistor is equal to sum of the resistances of all those multiple resistors.