Question

establish maximum power theorem

Answer 1

the maximum power transfer theorem states that, to obtain maximum external power from a source with a finite internal resistance, the resistance of the load must equal the resistance of the source as viewed from its output terminals. Moritz von Jacobi published the maximum power (transfer) theorem around 1840; it is also referred to as "Jacobi's law"

The theorem results in maximum power transfer, and not maximum efficiency. If the resistance of the load is made larger than the resistance of the source, then efficiency is higher, since a higher percentage of the source power is transferred to the load, but the magnitude of the load power is lower since the total circuit resistance goes up.



establish between current velocity and dirft
velocity ??
Let l is the length of the conductor and A uniforms area of cross-section.

Therefore, the volume of the conductor = Al

If n is the number of free electrons per unit volume of the conductor, then the total number of free electrons in the conductor=A/n.

If e is the charge on each electron then total charge on all the free electrons in the conductor

Q=A/ne                                     (1)

Let a constant potential differences V is applied across the ends of the conductor with the help of a battery

The electric field set up across the conductor is given by

E=V/l

Due to this field, the free electrons present in the conductor will begin to move with a drift velocity vd towards the left hand side of the conductor.

Thus the time taken by the free electrons to cross the conductor is

t=l/vd (2)

As current I=q/t                                                     (3)

By substituting equation (1) and (2) in equation (3),

We get

I=Alne/l/vd

Or                                      I=Anevd (4)

Since A,n and e are constant

I∞vd

Hence the current flowing through a conductor is directly proportional to the drift velocity.

Explanation and Example. In a conductor there are large number of free electrons. When we close the circuit , the electric field is established in the circuit with the speed of electromagnetic wave which causes electron drift at every portion of the circuit. Due to which the current is set up in the entire circuit instantly .The current thus set up does not wait for the electrons to flow from one end of the conductor to another end. It is due to this reason, the electric bulb glows immediately when switch is on.