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Next we can solve the remaining three equations and three unknown currents using a matrix approach,

Finally we find the power in the resistor,

P = 1Ω ( 44.1A) = 44W

5. ACTIVE DEVICES

•Active devices are different from passive devices such as resistors, capacitors and inductors. These devices are capable of changing their operational performance, may deliver power to the circuit, and can perform interesting mathematical functions.

•When doing most circuits problems we depends on idealized components. The following section will describe a number of components, thier models, and how to apply them in practical circuits.

5.1 OPERATIONAL AMPLIFIERS

• A very common and versatile device is the operational amplifier (Op-amp). They are characterized as,

-stable high gain amplifiers

-high input impedances

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-low output impdeances

•These are available for a few cents in commercial quantities. They also come in a wide variety of packages for various applications.

5.1.1 General Details

• The schematic symbol for these devices is given below,

+Vs

V-

-

Vo

V+

+

-Vs

• Inside these devices have a very high gain amplifier that compares the inputs and gives an output that is amplified as shown by,

Vo = G( V+ – V-)

where,

V- is the inverting input

V+ is the non-inverting input

G is the gain (typically 100000x) Vo is the output

Vs is the supply voltage

• When using these devices the circuit is typically set up so that both the inverting and non-invert- ing inputs have the same voltage, and the currents in to both of the inputs is negligable.