The maximum power delivered to the load is 9 W. Option A is the right choice.
The maximum power transfer theorem states that the maximum power transfer to a load occurs when the load impedance is the complex conjugate of the source impedance. In other words, the load impedance should be equal to 25 -j100 ohms.
In this circuit, the source impedance is 25 ohms + j100 ohms. The load impedance is 4.5 ohms + j18 ohms. The conjugate of the load impedance is 4.5 ohms - j18 ohms.
The power delivered to the load is calculated using the following equation:
P = V^2 / (4R)
where:
P is the power in watts
V is the voltage in volts
R is the resistance in ohms
In this case, the voltage is 45 volts and the resistance is 4.5 ohms - j18 ohms.
P = (45 volts)^2 / (4 * (4.5 ohms - j18 ohms))
P = 9 watts
Therefore, the maximum power delivered to the load is 9 watts. Option A is the right choice.
Question:-
For the circuit shown below, determine the maximum power delivered to the Load Z₁ if we require that the load can have any complex value?
A. 9 W
B. 4.5 W
C. 18 W
D. 2.25 W