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For maximum power transfer, according to maximum power transfer theorem, source impedance
- a)must be very must large as compared to the load impedance
- b)must be complex conjugate of load impedance
- c)must be equal to load impedance
- d)must be very much small as compared to the load impedance.
Correct answer is option 'B'. Can you explain this answer?
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Maximum Power Transfer Theorem
The maximum power transfer theorem states that the maximum power is transferred from a source to a load when the impedance of the source is equal to the complex conjugate of the load impedance. This theorem is applicable in electrical circuits when the goal is to maximize the power delivered to the load.
Explanation
In order to understand why the source impedance should be the complex conjugate of the load impedance for maximum power transfer, let's consider a simple circuit.
The Circuit
Assume a circuit with a source (represented by a voltage source in series with a source impedance) connected to a load (represented by a load impedance). The goal is to maximize the power transfer to the load.
Derivation
To derive the condition for maximum power transfer, we need to find the expression for power delivered to the load.
Power Delivered to the Load
The power delivered to the load can be calculated using the formula: P = V^2 / R, where V is the voltage across the load and R is the load resistance.
Voltage Across the Load
The voltage across the load can be determined using voltage division. According to voltage division, the voltage across the load is given by: V_load = V_source * (Z_load / (Z_source + Z_load)), where Z_load and Z_source are the load and source impedances, respectively.
Power Delivered to the Load (Cont.)
Substituting the expression for V_load into the power formula, we have: P = (V_source^2 * (Z_load^2 / (Z_source + Z_load)^2)) / R_load
Condition for Maximum Power Transfer
To maximize the power delivered to the load, we need to find the values of Z_source and Z_load that make the expression P maximum. To do this, we take the derivative of P with respect to Z_source and set it equal to zero.
After solving the equation, we find that the condition for maximum power transfer is: Z_source = Z_load*
Therefore, for maximum power transfer, the source impedance must be the complex conjugate of the load impedance.
Conclusion
In summary, the maximum power transfer theorem states that the source impedance should be the complex conjugate of the load impedance for maximum power transfer. By applying this theorem, we can ensure that the power delivered to the load is maximized in electrical circuits.
The maximum power transfer theorem states that the maximum power is transferred from a source to a load when the impedance of the source is equal to the complex conjugate of the load impedance. This theorem is applicable in electrical circuits when the goal is to maximize the power delivered to the load.
Explanation
In order to understand why the source impedance should be the complex conjugate of the load impedance for maximum power transfer, let's consider a simple circuit.
The Circuit
Assume a circuit with a source (represented by a voltage source in series with a source impedance) connected to a load (represented by a load impedance). The goal is to maximize the power transfer to the load.
Derivation
To derive the condition for maximum power transfer, we need to find the expression for power delivered to the load.
Power Delivered to the Load
The power delivered to the load can be calculated using the formula: P = V^2 / R, where V is the voltage across the load and R is the load resistance.
Voltage Across the Load
The voltage across the load can be determined using voltage division. According to voltage division, the voltage across the load is given by: V_load = V_source * (Z_load / (Z_source + Z_load)), where Z_load and Z_source are the load and source impedances, respectively.
Power Delivered to the Load (Cont.)
Substituting the expression for V_load into the power formula, we have: P = (V_source^2 * (Z_load^2 / (Z_source + Z_load)^2)) / R_load
Condition for Maximum Power Transfer
To maximize the power delivered to the load, we need to find the values of Z_source and Z_load that make the expression P maximum. To do this, we take the derivative of P with respect to Z_source and set it equal to zero.
After solving the equation, we find that the condition for maximum power transfer is: Z_source = Z_load*
Therefore, for maximum power transfer, the source impedance must be the complex conjugate of the load impedance.
Conclusion
In summary, the maximum power transfer theorem states that the source impedance should be the complex conjugate of the load impedance for maximum power transfer. By applying this theorem, we can ensure that the power delivered to the load is maximized in electrical circuits.
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