Question

what will be theeffective resistance in above circuit​

Answer 1

Answer:

In series circuit, the effective resistance is equal to sum of the resistances of individual components. So total resistance will be on higher side. In parallel circuit, reciprocal of effective resistance is equal to sum of reciprocals of individual resitances. So effective resistance is less.

Answer 2

Explanation:

The answer from Hashir Zahir is not very clear IMHO. He is confounding "effective resistance" with "equivalent resistance" or "Thévenin resistance" (in the Thévenin equivalent circuit) or "Norton resistance" (in the Norton equivalent circuit). In his example the equivalent resistance seen by the battery is 9 k Ω (calculated as 5+6||12 k Ω ; Hashir's expression is wrong).

The concept of effective resistance becomes interesting when related to reactive circuits, i.e. circuits including inductors or/and capacitors, working with variable voltages and currents (usually sinusoidal), and makes use of the concept of complex impedance. For instance, suppose we have a sinusoidal voltage generator which "sees" between its terminals (or is loaded by) a RL series circuit, whose complex impedance Z depends on the generators' frequency, ω , and is given by Z(ω)=Z=R+jωL , the sum of the complex impedances of the resistor and of the inductor.

The complex power is defined as S=VI∗=V2/Z∗ where V and I are the complex voltage and current (or phasors), representing the sinusoidal voltage and current in the generator, and the asterisk '*' indicates complex conjugate. The active or real power is the real part of S . Without loss of generality, we supposed in the above definition of S that V has zero phase, so that V=V∗ .

As I=V/(R+jωL) we can calculate I∗=Vexp(−jatan(ωL/R))/(R2+ω2L2) . Then S=V2exp(−jatan(ωL/R))/(R2+ω2L2) . The active power is P=R{S}=|S|cos(−atan(ωL/R)) which, after some algebra, leads to P=V2/[R(1+ω2L2/R)] .

Now, the concept of effective resistor Reff is defined as the (virtual) resistor that makes the real power equal to P=V2/Reff ; comparing with our reactive circuit we see that Reff=R(1+ω2L2/R) , which depends on the frequency, ω .

For other more general reactive circuits, the algebra would be more complicated but the concept would be the same: the effective resistance is the expression giving the (virtual) ohmic passive resistor which would dissipate the same real or active power that the reactive circuit is dissipating. If the load circuit is purely reactive (e.g. a LC series or parallel), then the active power and the effective resistor are both zero.