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I need to confirm something.Do circuits like the one shown below in which there is no connection between points A and B,treated as separate loops with no connection between them? enter image description here

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Yes, you can consider these loops separate when using mesh analysis.

Naming the loops 1, 2 and 3 from left to right and choosing CW for positive current flow you get:

$$ I_1 = \frac{5\text{V}}{R_x}\\ I_2 = 3V_x\\ I_3 = 3\text{A} $$

As you can see you have four unknowns, i.e. \$I_{1,2,3}\$ and \$V_x\$, but only three equations. Since you have a VCCS (voltage controlled current source) you should add an equation that relates its controlling parameter, \$V_x\$, with one or more loop currents. In this case:

$$ V_x = I_1R_x $$

Solving the linear system is now trivial.

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While there is not a direct connection between A and B, they are linked together.

The voltage across the resistor in the A loop is defined as Vx. There is a dependent voltage source in the B loop (directly under the B). That voltage source delivers 3Vx. Essentially, the voltage at B is 3 times the voltage at A.

Changing the A circuit will affect the B circuit.

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What you show here is an "equivalent circuit" and is generally only useful for analysis and understanding how electrical parts behave. In this case you have a "voltage-controlled current source" in the B loop, whose current will be 3 x Vx. Since Vx is 5V as shown, you get 15A from that current source.

This circuit as shown is not realizable directly, but is useful for understanding the behavior of circuits using things like transistor, which "behave" like voltage controlled current sources.

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