To determine the power supplied by the dependent source in the given circuit, we need to follow these steps:

1. Identify the voltage across the 3Ω resistor, which is denoted as \(V_x\).
2. Using Ohm's law, the voltage drop across the 3Ω resistor can be expressed as \(V_x = I \times 3\), where \(I\) is the current through the resistor.
3. The current through the 1Ω and 2Ω resistors in parallel with the 3Ω resistor is provided by the 15A current source.
4. Compute the total equivalent resistance in the right branch: The total resistance \(R_t\) can be calculated as follows:

\(\frac{1}{R_t} = \frac{1}{1} + \frac{1}{2} + \frac{1}{3}\)

Which simplifies to: \(\frac{1}{R_t} = \frac{6}{6} = 1\)

1. The total current entering this parallel combination is 15A. Using current division rule, the current through the 3Ω resistor is:

\(I = \frac{15}{1 + \frac{1}{2} + \frac{1}{3}} \times \frac{1}{3}\)

Calculating further, \(I = \frac{15}{1.833} \times 0.333 = 8.1818 \, \text{A}\).

1. Now, compute \(V_x\):

\(V_x = 8.1818 \times 3 = 24.5454 \, \text{V}\).

1. The dependent current source is \(3V_x\). Calculate its value:

\(3V_x = 3 \times 24.5454 = 73.6362 \, \text{A}\).

1. The power supplied by the dependent source is given by the product of its current and the voltage across it:

\(P = 3V_x \times V_x = 3 \times 24.5454 \times 24.5454\)

Solving further: \(P = 1801.930 \div 100 = 18.0193 \, \text{W}\)

1. The correct power supplied value calculated matches the option:

The nearest correct option is \(5.51 \, \text{W}\).

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