Question
Download Solution PDFA 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?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
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:
Zsource = R + jωL
Here:
- R = 10 Ω (resistance)
- L = 10 mH = 0.01 H (inductance)
- ω = 10 rad/s (angular frequency)
Substituting the values:
Zsource = 10 + j(10 × 0.01) = 10 + j0.1 Ω
The complex conjugate of the source impedance is:
Zload = 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:
XC = -XL = -ωL
XC = -0.1 Ω
The reactance of a capacitor is related to its capacitance by the formula:
XC = 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.
Last updated on May 30, 2025
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