A voltage source having source impedance of 10 ohm in series with 10 mH inductance generates a sinusoidal signal of amplitude 10 V and angular frequency 10 rad/s. What should be the load to get the maximum power transferred?

Explanation:

To achieve maximum power transfer, the load impedance must match the complex conjugate of the source impedance. In this problem, the source impedance is given as 10 Ω in series with 10 mH inductance. The complex impedance of the source can be expressed as:

Z_source = R + jωL

Here:

• R = 10 Ω (resistance)
• L = 10 mH = 0.01 H (inductance)
• ω = 10 rad/s (angular frequency)

Substituting the values:

Z_source = 10 + j(10 × 0.01) = 10 + j0.1 Ω

The complex conjugate of the source impedance is:

Z_load = R - jωL = 10 - j0.1 Ω 

To match this impedance, the load should consist of a 10 Ω resistor in series with a capacitive reactance that cancels out the inductive reactance of the source. The capacitive reactance is given by:

X_C = -X_L = -ωL

X_C = -0.1 Ω

The reactance of a capacitor is related to its capacitance by the formula:

X_C = 1 / (ωC)

Substituting the values:

-0.1 = 1 / (10 × C)

C = 1 / (10 × 0.1) = 1 F

Thus, the load impedance that matches the complex conjugate of the source impedance is a 10 Ω resistor in series with a 1 F capacitor. Therefore, the correct answer is Option 3.