In this article, we will study about Maximum Power Transfer Theorem. The Maximum Power is transferred in the circuit when the load impedance is matched with the source impedance. This theorem helps in increasing the efficiency and performance of the circuit.
The statement of Maximum Power Transfer Theorem is as follows: It states that the maximum power is developed in a load when the load resistance equals the Thevenin resistance of the source to which it is connected. To achieve power transfer in a circuit, the resistance or impedance of the load must match with the source impedance.
1) The battery has a maximum power it can provide. For example, if this power is P = 100 W, then since P = RI^2 the current will be I = (P/R)^0.5 = 31.6 amps and the voltage V = RI = 3.16 V. 2) The battery has a maximum current it can provide. For example, if this current is I = 5 A, then V = RI = 0.5 V.
For maximum power transfer, we will equate the above equation to zero: RL + Rth = 2RL RL = Rth Hence, in an AC circuit, the highest power transfer occurs when the load resistor (RL) equals the Thevenin resistance (Rth) and XL equals the negative of Xth.
For a passive setup, maximum power is transferred to the load when the impedance of the load equals the complex conjugate of the corresponding impedance observed from the load's terminals. Now let us derive the condition for maximum power transfer in the AC circuits: Consider an equivalent circuit analogous to Thevenin's.
A refinement of the maximum power theorem says that any reactive components of source and load should be of equal magnitude but opposite sign. (See below for a derivation.) This means that the source and load impedances should be complex conjugates of each other. In the case of purely resistive circuits, the two concepts are identical.
How do you calculate maximum transfer of power in a rheostat?
For maximum transfer of power the external resistance connected to the source should be equal to the internal resistance of the source R=r P M ax = (R+r)2E2R = 4R2E2R P Max = 4RE2 Illustration: A 20 V battery of internal resistance of 4 is connected to a rheostat.